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Iniguez-Goizueta, Ainhoa. "Word fibres in finite p-groups and pro-p groups." Thesis, University of Oxford, 2016. https://ora.ox.ac.uk/objects/uuid:3a9cfc11-d171-4876-82b3-7dff012c3a70.
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Snopçe, Ilir. "Lie methods in pro-p groups." Diss., Online access via UMI:, 2009.
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Martin, Maria Eugenia. "Propriedades homologicas de grupos pro-p." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306927.
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Orientador: Dessislava Hristova KochloukovaDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: Nesta dissertação discutimos propriedades homológicas de grupos discretos e grupos pro-p. Em particular trabalhamos com grupos abstratos de dualidade de Poincaré orientáveis de dimensão três e seu completamento pro-p. Os primeiros capítulos da dissertação incluem uma exposição sobre as propriedades homológicas básicas de grupos abstratos e grupos pro-p. Finalmente, descrevemos um resultado recente de [KZ], publicado em Transactions MAS ( 2008), que clássica quando o completamento pro-p de um grupo de dualidade de Poincaré orientável de dimensão três de um grupo pro-p de dualidade de Poincaré orientável de dimensão três
Abstract: In this dissertation we discuss homological properties of discrete groups and pro-p groups. In particular we work with groups of abstract of Poincaré duality of dimension three steerable and its pro-p completion. The first chapters of the dissertation include a presentation on the basic homological properties of abstract groups and pro-p groups. Finally, we describe a recent result of [KZ], published in Transactions AMS (2008), which ranks as the pro-p completion of a group of Poincare-steerable dual dimension of three is a group of pro-p duality of Poincare -steerable in three dimensions
Mestrado
Mestre em Matemática
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Pinto, Aline Gomes da Silva. "Propriedades homologicas de grupos pro-p." [s.n.], 2005. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306931.
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Orientador: Dessislava H. KochloukovaTese (doutorado) - Universidade Estadual de Campinas. Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: Neste trabalho, provamos dois resultados sobre propriedades homológicas de grupos pro-p. O primeiro responde positivamente à conjectura de J. King que afirma que, se G é um grupo pro-p metabeliano finitamente gerado e m um inteiro positivo, então G mergulha como subgrupo fechado em um grupo pro-p metabeliano de tipo homológico F Pm. O segundo resultado caracteriza módulos pro-p B de tipo homológico F P m sobre [[ZpG]], onde G é um grupo pro-p metabeliano topologicamente finitamente gerado, dado pela extensão de um grupo pro-p abeliano A por um grupo pro-p abeliano Q, e B é um [[ZpQ]]-módulo pro-p finitamente gerado que é visto como um [[ZpG]]-módulo pro-p via a projeção de G -t Q. A caracterização é dada em termos do invariante para grupos pro-p metabelianos introduzido por J. King [15] e é uma generalização do caso onde B = Zp é o anel de inteiros p-ádicos considerado como G-módulo trivial, que dá a classificação dos grupos pro-p metabelianos de tipo homológico FPm, provado por D. Kochloukova [18]
Abstract: In this work, we prove two results about homological properties of metabelian pro-p groups. The first one answers positively a conjecture suggested by J. King that, if G is a finitely generated metabelian pro-p group and m a positive integer, G embeds in a metabelian pro-p group of homological type F P m. The second result caracterize the modules B of homological type F P mover [[ZpG]], where G is a topologically finitely generated metabelian pro-p group that is an extension of A by Q, with A and Q abelian, and B is a finitely generated pro-p [[ZpQ]]-module that is viewed as a pro-p [[ZpG]]-module via the projection G -f Q. The characterization is given in terms of the invariant introduced by J. King [15] and is a generalization of the case when B = Zp is considered as a trivial [[ZpG]]-module, that gives the classification of metabelian pro-p groups of type FPm, proved by D. Kochloukova [18]
Doutorado
Matematica
Doutor em Matemática
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Rêgo, Yuri Santos 1989. "A desigualdade de Golod-Safarevic para grupos pro-p e grupos abstratos." [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306920.
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Orientador: Dessislava Hristova KochloukovaDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica
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Resumo: Neste trabalho estuda-se os principais resultados dados por J. Wilson no artigo "Finite Presentations of Pro-p Groups and Discrete Groups", relacionados à Desigualdade de Golod-¿afarevi? para uma ampla classe de grupos pro-p e abstratos infinitos. Apresentamos a teoria básica de grupos livres abstratos, levando à noção de apresentação de grupos, com foco em apresentações finitas. É feito um estudo sobre grupos profinitos, particularmente no caso pro-p. Abrange-se definições, propriedades algébricas e topológicas básicas, bem como o caso de finitos geradores com o subgrupo de Frattini, e conceitos de completamentos, de grupos pro-p livres, de apresentações de grupos pro-p e de álgebras de grupo completas. No capítulo final estudamos os resultados principais para grupos pro-p e abstratos finitamente apresentáveis, que incluem grupos solúveis e implicações na estrutura de certos grupos satisfazendo a Desigualdade. Os anexos relacionam a teoria aqui apresentada a grupos pro-p de posto finito e homologia e cohomologia de grupos pro-p
Abstract: In this work we study the main results presented by J. Wilson in his paper "Finite Presentations of Pro-p Groups and Discrete Groups", which extend the Golod-¿afarevi? Inequality to a large class of infinite pro-p and abstract groups. In the first chapter we present the basic theory of abstract free groups, focusing on finite presentations. Next we study profinite groups, with focus on pro-p groups. This study ranges from definitions to basic algebraic and topological properties, as well as the cases of finitely generated groups and the Frattini subgroup, and notions of completion, free pro-p groups, presentations of pro-p groups and completed group algebras. In the last chapter we study the main results regarding finite presentations of pro-p and abstract groups, which include soluble groups and implications on the structure of certain groups for which the Inequality holds. In the appendixes we briefly relate the presented theory to pro-p groups of finite rank and homology and cohomology of pro-p groups
Mestrado
Matematica
Mestre em Matemática
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King, Jeremy David. "Finite presentability of Lie algebras and pro-p groups." Thesis, University of Cambridge, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.364385.
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Lima, Igor dos Santos 1983. "Completamentos Pro-p de grupos de dualidade de Poincaré." [s.n.], 2012. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306926.
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Orientador: Dessislava Hristova KochloukovaTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica
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Resumo: Neste trabalho, nos Teoremas Principais, damos condições suficientes para que o completamento pro-p de um grupo abstrato PDn seja virtualmente um grupo pro-p PDs para algum s ? n - 2 com n ? 4. Esse resultado é uma generalização do Teorema 3 em [K-2009]. Nossa prova é baseada em [K-2009] e nos resultados de A. A. Korenev [Ko-2004] e [Ko-2005]. Além disso, damos alguns exemplos de grupos que satisfazem as condições dos Teoremas Principais
Abstract: In this work we give in the Main Theorems suffiient conditions for that the pro- p completion of an abstract orientable PDn group to be virtually a pro-p PDs group for some s ? n - 2 with n ? 4. This result is a generalization of the Theorem 3 in [K-2009]. Our proof is based on [K-2009] and on the results of A. A. Korenev [Ko-2004] and [Ko-2005]. Furthermore we give some examples of groups that satisfy the conditions of the Main Theorems
Doutorado
Matematica
Doutor em Matemática
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Middleton, Sarah E. A. P. "Hereditarily just infinite profinite groups that are not virtually pro-p." Thesis, Royal Holloway, University of London, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.604025.
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A profinite group G is just infinite if it is infinite and every non- trivial closed normal subgroup of G is open, and hereditarily just infinite if every open subgroup is just infinite. Hereditarily just infinite profinite groups that are not virtually pro-p were first described by J. S. Wilson, in his recent paper 'Large hereditarily just infinite groups', in 2010. These profinite groups are inverse limits of finite groups that arc iterated wreath products. The iterated wreath products are constructed from finite non-abelian simple groups, using two types of transitive actions; one of which is specified and the other is left unspecified.
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Smith, Duncan Alexander Mathematics UNSW. "The Families with Period 1 of 2-groups of Coclass 3." Awarded by:University of New South Wales. Mathematics, 2000. http://handle.unsw.edu.au/1959.4/17792.
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The 2-groups of coclass 1 are widely known and James (in 1975) looked at the 2-groups of coclass 2. Development of the p-group generation algorithm implemented by O'Brien at ANU enabled group presentations to be provided for the 2-groups of coclass 3 by Newman and O'Brien for groups of order up to 223. Newman and O'Brien (in 1999) conjectured the number of descendants of 2n for all n. They introduced the concept of a family, with each family related to a different pro-p-group and the concept of a sporadic p-group, a p-group external to any family. They found 1782 sporadic 2-groups with order at most 214. The 70 families of 2-groups of coclass 3 can be further split according to their period, a measure of the repetitive structure of the families. Newman and O'Brien conjectured that these families had periods of 1, 2 or 4. This thesis examines the 2-groups of coclass 3 contained in families with period 1 and shows that the number of descendants conjectured by Newman and O'Brien is correct. Furthermore the presentation of all groups contained in period 1 families is provided and shown to be correct.
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Gärtner, Jochen [Verfasser], and Kay [Akademischer Betreuer] Wingberg. "Mild pro-p-groups with trivial cup-product / Jochen Gärtner ; Betreuer: Kay Wingberg." Heidelberg : Universitätsbibliothek Heidelberg, 2011. http://d-nb.info/1179782801/34.
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Toinet, Emmanuel. "Automorphisms of right-angled Artin groups." Thesis, Dijon, 2012. http://www.theses.fr/2012DIJOS003.
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Cette thèse a pour objet l’étude des automorphismes des groupes d’Artin à angles droits. Etant donné un graphe simple fini G, le groupe d’Artin à angles droits GG associé à G est le groupe défini par la présentation dont les générateurs sont les sommets de G, et dont les relateurs sont les commutateurs [v,w], où {v,w} est une paire de sommets adjacents. Le premier chapitre est conçu comme une introduction générale à la théorie des groupes d’Artin à angles droits et de leurs automorphismes. Dans un deuxième chapitre, on démontre que tout sous-groupe sous-normal d’indice une puissance de p d’un groupe d’Artin à angles droits est résiduellement p-séparable. Comme application de ce résultat, on montre que tout groupe d’Artin à angles droits est résiduellement séparable dans la classe des groupes nilpotents sans torsion. Une autre application de ce résultat est que le groupe des automorphismes extérieurs d’un groupe d’Artin à angles droits est virtuellement résiduellement p-fini. On montre également que le groupe de Torelli d’un groupe d’Artin à angles droits est résiduellement nilpotent sans torsion, et, par suite, résiduellement p-fini et bi-ordonnable. Dans un troisième chapitre, on établit une présentation du sous-groupe Conj(GG) deAut(GG) formé des automorphismes qui envoient chaque générateur sur un conjugué de lui-mêmeThe purpose of this thesis is to study the automorphisms of right-angled Artin groups. Given a finite simplicial graph G, the right-angled Artin group GG associated to G is the group defined by the presentation whose generators are the vertices of G, and whose relators are commuta-tors of pairs of adjacent vertices. The first chapter is intended as a general introduction to the theory of right-angled Artin groups and their automor-phisms. In a second chapter, we prove that every subnormal subgroup ofp-power index in a right-angled Artin group is conjugacy p-separable. As an application, we prove that every right-angled Artin group is conjugacy separable in the class of torsion-free nilpotent groups. As another applica-tion, we prove that the outer automorphism group of a right-angled Artin group is virtually residually p-finite. We also prove that the Torelli group ofa right-angled Artin group is residually torsion-free nilpotent, hence residu-ally p-finite and bi-orderable. In a third chapter, we give a presentation of the subgroup Conj(GG) of Aut(GG) consisting of the automorphisms thats end each generator to a conjugate of itself
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Blondeau, Julien. "Déformation des extensions peu ramifiées en P." Phd thesis, Université de Franche-Comté, 2011. http://tel.archives-ouvertes.fr/tel-00936135.
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Simons, Nicholas James. "The width of verbal subgroups in profinite groups." Thesis, University of Oxford, 2009. http://ora.ox.ac.uk/objects/uuid:01075c36-c7e6-4def-9647-86b4346e4726.
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The main result of this thesis is an original proof that every word has finite width in a compact $p$-adic analytic group. The proof we give here is an alternative to Andrei Jaikin-Zapirain's recent proof of the same result, and utilises entirely group-theoretical ideas. We accomplish this by reducing the problem to a proof that every word has finite width in a profinite group which is virtually a polycyclic pro-$p$ group. To obtain this latter result we first establish that such a group can be embedded as an open subgroup of a group of the form $N_1M_1$, where $N_1$ is a finitely generated closed normal nilpotent subgroup, and $M_1$ is a finitely generated closed nilpotent-by-finite subgroup; we then adapt a method of V. A. Romankov. As a corollary we note that our approach also proves that every word has finite width in a polycyclic-by-finite group (which is not profinite). As a supplementary result we show that for finitely generated closed subgroups $H$ and $K$ of a profinite group the commutator subgroup $[H,K]$ is closed, and give examples to show that various hypotheses are necessary. This implies that the outer-commutator words have finite width in profinite groups of finite rank. We go on to establish some bounds for this width. In addition, we show that every word has finite width in a product of a nilpotent group of finite rank and a virtually nilpotent group of finite rank. We consider the possible application of this to soluble minimax groups.
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Hubbard, David. "The nonexistence of certain free pro-p extensions and capitulation in a family of dihedral extensions of Q /." Thesis, Connect to this title online; UW restricted, 1996. http://hdl.handle.net/1773/5734.
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Higashiyama, Kazumi. "The semi-absolute anabelian geometry of geometrically pro-p arithmetic fundamental groups of associated low-dimensional configuration spaces." Kyoto University, 2019. http://hdl.handle.net/2433/242582.
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Schmidt, Nicolas Alexander. "Generic pro-p Hecke algebras, the Hecke algebra of PGL(2, Z), and the cohomology of root data." Doctoral thesis, Humboldt-Universität zu Berlin, 2019. http://dx.doi.org/10.18452/19724.
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Es wird die Theorie der generischen pro-$p$ Hecke-Algebren und ihrer Bernstein-Abbildungen entwickelt. Für eine Unterklasse diese Algebren, der \textit{affinen} pro-$p$ Hecke-Algebren wird ein Struktursatz bewiesen, nachdem diese Algebren unter anderem stets noethersch sind, wenn es der Koeffizientenring ist. Hilfsmittel ist dabei der Nachweis der Bernsteinrelationen, der in abstrakter Weise geführt wird und so die bestehende Theorie verallgemeinert.
Ferner wird der top. Raum der Orientierungen einer Coxetergruppe eingeführt und im Falle der erweiterten modularen Gruppe $\operatorname{PGL}_2(\mathds{Z})$ untersucht, und ausgenutzt um Kenntnisse über die Struktur der zugehörigen Hecke-Algebra als Modul über einer gewissen Unteralgebra, welche zur Spitze im Unendlichen zugeordnet ist, zu erlangen.
Schließlich wird die Frage des Zerfallens des Normalisators eines maximalen zerfallenden Torus innerhalb einer zerfallenden reduktiven Gruppe als Erweiterung der Weylgruppe durch die Gruppe der rationalen Punkte des Torus untersucht, und mittels zuvor erreichter Ergebnisse auf eine kohomologische Frage zurückgeführt. Zur Teilbeantwortung dieser werden dann die Kohomologiegruppen bis zur Dimension drei der Kocharaktergitter der fasteinfachen halbeinfachen Wurzeldaten einschließlich des Rangs 8 berechnet. Mittels der Theorie der $\mathbf{FI}$-Moduln wird daraus die Berechnung der Kohomologie der mod-2-Reduktion der Kowurzelgitter für den Typ $A$ in allen Rängen bewiesen.The theory of generic pro-$p$ Hecke algebras and their Bernstein maps is developed. For a certain subclass, the \textit{affine} pro-$p$ Hecke algebras, we are able to prove a structure theorem that in particular shows that the latter algebras are always noetherian if the ring of coefficients is. The crucial technical tool are the Bernstein relations, which are proven in an abstract way that generalizes the known cases. Moreover, the topological space of orientations is introduced and studied in the case of the extended modular group $\operatorname{PGL}_2(\mathds{Z})$, and used to determine the structure of its Hecke algebra as a module over a certain subalgebra, attached to the cusp at infinity. Finally, the question of the splitness of the normalizer of a maximal split torus inside a split reductive groups as an extension of the Weyl group by the group of rational points is studied. Using results obtained previously, this questioned is then reduced to a cohomological one. A partial answer to this question is obtained via computer calculations of the cohomology groups of the cocharacter lattices of all almost-simple semisimple root data of rank up to $8$. Using the theory of $\mathbf{FI}$-modules, these computations are used to determine the cohomology of the mod 2 reduction of the coroot lattices for type $A$ and all ranks.
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QUADRELLI, CLAUDIO. "Cohomology of Absolute Galois Groups." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2014. http://hdl.handle.net/10281/56993.
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The main problem this thesis deals with is the characterization of profinite groups which are realizable as absolute Galois groups of fields: this is currently one of the major problems in Galois theory. Usually one reduces the problem to the pro-p case, i.e., one would like to know which pro-p groups occur as maximal pro-p Galois groups, i.e., maximal pro-p quotients of absolute Galois groups. Indeed, pro-p groups are easier to deal with than general profinite groups, yet they carry a lot of information on the whole absolute Galois group.
We define a new class of pro-p groups, called Bloch-Kato pro-p group, whose Galois cohomology satisfies the consequences of the Bloch-Kato conjecture. Also we introduce the notion of cyclotomic orientation for a pro-p group. With this approach, we are able to recover new substantial information about the structure of maximal pro-p Galois groups, and in particular on theta-abelian pro-p groups, which represent the "upper bound" of such groups.
Also, we study the restricted Lie algebra and the universal envelope induced by the Zassenhaus filtration of a maximal pro-p Galois group, and their relations with Galois cohomology via Koszul duality.
Altogether, this thesis provides a rather new approach to maximal pro-p Galois groups, besides new substantial results.
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Heyer, Claudius. "Applications of parabolic Hecke algebras: parabolic induction and Hecke polynomials." Doctoral thesis, Humboldt-Universität zu Berlin, 2019. http://dx.doi.org/10.18452/20137.
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Im ersten Teil wird eine neue Konstruktion der parabolischen Induktion für pro-p Iwahori-Heckemoduln gegeben. Dabei taucht eine neue Klasse von Algebren auf, die in gewisser Weise als Interpolation zwischen der pro-p Iwahori-Heckealgebra einer p-adischen reduktiven Gruppe $G$ und derjenigen einer Leviuntergruppe $M$ von $G$ gedacht werden kann. Für diese Algebren wird ein Induktionsfunktor definiert und eine Transitivitätseigenschaft bewiesen. Dies liefert einen neuen Beweis für die Transitivität der parabolischen Induktion für Moduln über der pro-p Iwahori-Heckealgebra. Ferner wird eine Funktion auf einer parabolischen Untergruppe untersucht, die als Werte nur p-Potenzen annimmt. Es wird gezeigt, dass sie eine Funktion auf der (pro-p) Iwahori-Weylgruppe von $M$ definiert, und
dass die so definierte Funktion monoton steigend bzgl. der Bruhat-Ordnung ist und einen Vergleich der Längenfunktionen zwischen der Iwahori-Weylgruppe von $M$ und derjenigen der Iwahori-Weylgruppe von $G$ erlaubt.
Im zweiten Teil wird ein allgemeiner Zerlegungssatz für Polynome über der sphärischen (parahorischen) Heckealgebra einer p-adischen reduktiven Gruppe $G$ bewiesen. Diese Zerlegung findet über einer parabolischen Heckealgebra statt, die die Heckealgebra von $G$ enthält. Für den Beweis des Zerlegungssatzes wird vorausgesetzt, dass die gewählte parabolische Untergruppe in einer nichtstumpfen enthalten ist. Des Weiteren werden die nichtstumpfen parabolischen Untergruppen von $G$ klassifiziert.The first part deals with a new construction of parabolic induction for modules over the pro-p Iwahori-Hecke algebra. This construction exhibits a new class of algebras that can be thought of as an interpolation between the pro-p Iwahori-Hecke algebra of a p-adic reductive group $G$ and the corresponding algebra of a Levi subgroup $M$ of $G$. For these algebras we define a new induction functor and prove a transitivity property. This gives a new proof of the transitivity of parabolic induction for modules over the pro-p Iwahori-Hecke algebra. Further, a function on a parabolic subgroup with p-power values is studied. We show that it induces a function on the (pro-p) Iwahori-Weyl group of $M$, that it is monotonically increasing with respect to the Bruhat order, and that it allows to compare the length function on the Iwahori-Weyl group of $M$ with the one on the Iwahori-Weyl group of $G$. In the second part a general decomposition theorem for polynomials over the spherical (parahoric) Hecke algebra of a p-adic reductive group $G$ is proved. The proof requires that the chosen parabolic subgroup is contained in a non-obtuse one. Moreover, we give a classification of non-obtuse parabolic subgroups of $G$.
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Salle, Landry. "Présentation de groupes de Galois de pro-p-extensions de corps de nombres." Toulouse 3, 2008. http://thesesups.ups-tlse.fr/862/.
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L'objet de cette thèse est la détermination de nouvelles situations dans lesquelles des invariants algébriques d'un groupe de Galois d'une pro-p-extension de corps de nombres peuvent être estimés. On considère d'abord des groupes de Galois d'extensions à ramification contrôlée au-dessus de la -extension cyclotomique d'un corps de nombres. Par la théorie du corps de classes, on généralise des résultats de Jaulent sur le -rang de l'abélianisé d'un tel groupe, puis on montre que les techniques de Chafarevitch et Koch s'appliquent ici pour obtenir une estimation du nombre de générateurs et une majoration du nombre de relations des groupes considérés. On introduit en particulier un nouveau groupe " de Kummer ", qui contrôle un défaut de principe local-global, et on donne quelques conditions suffisantes pour sa trivialité. La seconde partie a pour objet d'identifier des groupes de Galois qui soient " cléments " : ces groupes, introduits dans ce contexte par Labute, ont une dimension cohomologique inférieure à 2. On généralise des résultats de Wingberg sur les groupes à ramification et décomposition contrôlées, et on exhibe de tels groupes dans le cas de la ramification mixte. Les techniques employées s'appliquent aussi au cas des corps de fonctions. Enfin, on se concentre sur le cas où p=2 au-dessus d'un corps quadratique imaginaire. Après avoir généralisé des résultats de Ferrero et Kida sur les invariants d'Iwasawa au cas de la ramification modérée, on donne dans certains cas une présentation du groupe de Galois de la pro-2-extension S-ramifiée maximale de la -extension cyclotomique du corps de base, en reprenant une méthode introduite par Mizusawa dans le cas non ramifiéIn this thesis we determine new situations where some algebraic invariants of the Galois group of a pro-p-extension of a number field can be estimated. First we consider the Galois groups of extensions with restricted ramification above the cyclotomic -extension of a number field. By class field theory, we generalize Jaulent's results on the -rank of the abelianization of such a group. Then, we make use of Chafarevitch and Koch's methods to give the number of generators and to bound the number of relations. We are led to introduce a so-called Kummer group, which gives a bound of the defect of a local-global principle, and we find some sufficient conditions to annihilate it. In the second part, we intend to find some new mild pro-p-groups : such groups, which have been studied in an arithmetical setting by Labute, have cohomological dimension lower than 2. We generalize results by Wingberg on groups with restricted ramification and prescribed decomposition. In particular, such groups are exhibited in the case of mixed ramification. The method applies as well in the case of function fields. In the last part we focus on the case p=2 with an imaginary quadratic field as a base field. First we generalize results of Ferrero and Kida on Iwasawa invariants to the case of tamely ramified extensions. Then we give, in some special cases, a presentation of the Galois group of the maximal S-ramified pro-2-extension over the cyclotomic-extension of the base field, using a method of Mizusawa
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Rougnant, Marine. "Sur quelques aspects des extensions à ramification restreinte." Thesis, Bourgogne Franche-Comté, 2018. http://www.theses.fr/2018UBFCD015/document.
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Soit p un nombre premier, soit K/k une extension galoisienne finie de corps de nombres de degré premier à p et soit S un ensemble fini de premiers de k. Le groupe de Galois G(K,S) de la pro-p extension maximale de K non ramifiée en dehors de S est l'objet central de ce mémoire.On se place dans un premier temps dans le cas modéré : on suppose que S ne contient pas les places divisant p. Les travaux combinés de Labute, Minac et Schmidt sur les pro-p groupes mild ont permis d'exhiber les premiers exemples de groupes G(K,S) de dimension cohomologique 2. En implémentant un corollaire de leur critère dans le logiciel PARI/GP, on observe un phénomène de propagation : si k=Q et si le groupe G(Q,S) est mild, un fort pourcentage des groupes G(K,S) l'est également, pour K quadratique imaginaire. En associant au groupe G(K,S) deux graphes orientés dont les arcs sont définis par la ramification dans des extensions p-élémentaires, on démontre un critère théorique pour que ce phénomène de propagation ait lieu.On considère ensuite le cas sauvage : toutes les places au-dessus de p sont contenues dans S. Le groupe de Galois Δ:=Gal(K/k) agit sur G(K,S) ; on note G le plus grand quotient de G(K,S) sur lequel Δ agit trivialement et H le sous-groupe fermé de G(K,S) correspondant. Maire a étudié la liberté du Zp[[G]]-module H^{ab}. Nous poussons plus loin ses résultats en considérant les φ-composantes de H^{ab} sous l'action de Δ. Sous de bonnes hypothèses et sous la conjecture de Leopoldt, on démontre une condition nécessaire et suffisante pour que les φ-composantes soient libres ou non. La théorie du corps de classes permet de ramener cette condition à l'étude du régulateur normalisé, et donc à la p-rationalité du corps K. Les expérimentations faites sur PARI/GP dans des familles d'extensions cubiques cycliques, diédrales et cycliques de degré 4 du corps des rationnels corroborent une conjecture de Gras selon laquelle tout corps de nombres est p-rationnel pour p suffisant grandLet p be a prime number, let K/k be a Galois extension of number fields and let S be a finite set of primes of K. We suppose that the degree of K/k is finite and coprime to p. We denote by G(K,S) the Galois group of the pro-p maximal extension of K unramified outside S. We focus on this thesis on two differents aspects of this pro-p group.We are first interested in the tame case : we suppose that S does not contain any place above p. The works of Labute, Minac and Schmidt about mild pro-p groups brought the first examples of groups G(K,S) of cohomological dimension two. Using a corollary of their criterium, we compute some examples with PARI/GP and we observe a propagation phenomenum : if we take K=Q and if we suppose that G(Q,S) is mild, a large part of the pro-p groups G(K,S) with K imaginary quadratic are mild too. We then associate two oriented graphs to G(K,S) and we show a theoretical criterium proving mildness of some imaginary quadratic fields.We then consider the wild case where all the places dividing p belong to S. The Galois group Δ:=Gal(K/k) acts on G(K,S). The action of Δ is trivial on some quotients of G(K,S) ; we denote by G the maximal one and by H the corresponding closed subgroup of G(K,S). Maire has studied the Zp[[G]]-freeness of the module H^{ab}. We extend his results considering the φ-component of H^{ab} under the action of Δ. In a favourable context and under Leopoldt's conjecture, we show a necessary and sufficient condition for the freeness of the φ-components. This condition is connected to p-rational fields by class field theory. We present experiments with PARI/GP in some families of cubic cyclic, dihedral and quartic cyclic extensions of Q which support the following conjecture from Gras : every number field is p-rational for sufficiently large p
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Ollivier, Rachel. "Modules sur l'algèbre de Hecke du pro-p-Iwahori de groupe linéaire général à coefficients dans F en caractéristique p." Paris 7, 2005. http://www.theses.fr/2005PA077162.
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Toinet, Emmanuel. "Automorphismes des groupes d'Artin à angles droits." Phd thesis, Université de Bourgogne, 2012. http://tel.archives-ouvertes.fr/tel-00698614.
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Cette thèse a pour objet l'étude des automorphismes des groupes d'Artin à angles droits. Etant donné un graphe simple fini $\Gamma$, le groupe d'Artin à angles droits $G_\Gamma$ associé à $\Gamma$ est le groupe défini par la présentation dont les générateurs sont les sommets de $\Gamma$, et dont les relateurs sont les commutateurs $[v,w]$, où {$v$,$w$} est une paire de sommets adjacents. Le premier chapitre est conçu comme une introduction générale à la théorie des groupes d'Artin à angles droits et de leurs automorphismes. Dans un deuxième chapitre, on démontre que tout sous-groupe sous-normal d'indice une puissance de $p$ d'un groupe d'Artin à angles droits est résiduellement $p$-séparable. Comme application de ce résultat, on montre que tout groupe d'Artin à angles droits est résiduellement séparable dans la classe des groupes nilpotents sans torsion. Une autre application de ce résultat est que le groupe des automorphismes extérieurs d'un groupe d'Artin à angles droits est virtuellement résiduellement $p$-fini. On montre également que le groupe de Torelli d'un groupe d'Artin à angles droits est résiduellement nilpotent sans torsion, et, par suite, résiduellement $p$-fini et bi-ordonnable. Dans un troisième chapitre, on établit une présentation du sous-groupe $Conj(G_\Gamma)$ de $Aut(G_\Gamma)$ formé des automorphismes qui envoient chaque générateur sur un conjugué de lui-même.
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Lima, Jeyson Ferreira Silva de. "Pra?as p?blicas caicoense: territorialidades, sociabilidades e identidades." Universidade Federal do Rio Grande do Norte, 2013. http://repositorio.ufrn.br:8080/jspui/handle/123456789/18949.
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Previous issue date: 2013-03-18Conselho Nacional de Desenvolvimento Cient?fico e Tecnol?gico
The city, with all its complexity, is marked by the different uses that emerge and give the current composition of its forms, functions, processes and structures (SANTOS, 2008). These uses are responsible for defining the territoriality that engender public squares, especially from the projection of the practices of sociability and pleasure experienced by social groups and urban households, giving rise to the emergence of agreements and conflicts, especially when the public sphere and negotiates a private residence in the same territory. Thus, from analyzes performed in the public squares of the city of Caico / RN in the current context, did a survey of territorialities undertaken by these groups and social aggregates. These squares were seized territories while public use, but marked by the presence of private, becoming as important elements of the urban space caicoense
A cidade, com toda a sua complexidade, ? marcada pelos diferentes usos que se esbo?am e que d?o a composi??o atual de suas formas, fun??es, processos e estruturas (SANTOS, 2008). Estes usos s?o respons?veis por definir as territorialidades que se engendram nas pra?as p?blicas, sobretudo a partir da proje??o das pr?ticas de sociabilidade e de lazer vivenciadas pelos grupos e agregados sociais urbanos, dando margem ao surgimento de acordos e conflitos, especialmente, quando a esfera p?blica e a privada negocia a perman?ncia no mesmo territ?rio. Assim, a partir de an?lises realizadas nas pra?as p?blicas da cidade de Caic?/RN no contexto atual, fizemos um exame das territorialidades empreendidas por estes grupos e agregados sociais. Tais pra?as foram apreendidas enquanto territ?rios de uso p?blico, por?m marcados pela presen?a privada, configurando-se enquanto importantes elementos constituintes do espa?o urbano caicoense
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Validire, Romain. "Capitulation des noyaux sauvages étales." Phd thesis, Université de Limoges, 2008. http://tel.archives-ouvertes.fr/tel-00343427.
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Ce travail de thèse porte sur deux problèmes distincts, tous deux en lien avec le comportement galoisien de certains noyaux de localisation en cohomologie étale : les noyaux sauvages étales. Fixons un nombre premier p et $F_{\infty}$ une $\Z_p$-extension d'un corps de nombres $F$.La structure de groupe abélien du p-groupe des classes des étages de $F_{\infty}/F$ est asymptotiquement bien connue : nous montrons, au moyen de la théorie d'Iwasawa des $\Z_p$-extensions, un analogue de ce résultat en $K$-théorie supérieure.
Dans un deuxième temps, nous étudions le groupe de Galois sur $F_{\infty}$ de la pro-p-extension, non ramifiée, p-décomposée maximale de $F_{\infty}$, lorsque $F_{\infty}$ est la $\Z_p$-extension cyclotomique de $F$. Après avoir établi un lien entre la structure de ce groupe et le comportement galoisien des noyaux sauvages étales, nous donnons divers critères effectifs de non pro-p-liberté pour ce groupe.
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Montenegro, Guzmán Samaria. "Théorie des modèles des corps pseudo-réels clos et pseudo-p-adiquement clos." Sorbonne Paris Cité, 2015. http://www.theses.fr/2015USPCC269.
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Ceci est une thèse en théorie des modèles appliquée à l'algèbre. Dans cette thèse nous étudions la théorie des corps pseudo-réels clos (corps PRC) et pseudo-p-adiquement clos (corps PpC) bornés d'un point de vue modèle-théorique. Les corps PRC et PpC sont des généralisations des corps pseudo-algébriquement clos (corps PAC), des corps réels clos, et des corps p-adiquement clos. Le résultat principal de cette thèse est une réponse positive à la conjecture de Chernikov, Kaplan et Simon : Si M est un corps PRC, alors M est borné si et seulement si Th(M) est NTP2. Dans le cas des corps PpC nous prouvons que si M est un corps PpC borné, alors Th(M) est NTP2. Nous généralisons également ce résultat pour obtenir que si M est un corps PRC (respectivement PpC) borné avec exactement n ordres (respectivement n valuations p-adiques), alors Th(M) est forte de fardeau n. Ceci permet également de calculer explicitement le fardeau des types et de décrire la déviation. D'autres résultats importants sont des résultats d'amalgamation de types et l'élimination des imaginaires pour les corps PRC bornésThis is a thesis in model theory applied to algebra. In this thesis we study the theory of bounded pseudo real closed fields (PRC fields) and pseudo p-adically closed fields (PpC fields) from a model theoretic point of view. The classes of bounded PRC and PpC fields are generalizations of those of pseudo-algebraically closed fields (PAC fields), real closed fields, and p-adically closed fields. The main result of the thesis is a positive answer to the conjecture by Chernikov, Kaplan and Simon: If M is a PRC-field, then Th(M) is NTP2 if and only if M is bounded. In the case of PpC fields, we prove that if M is a bounded PpC field, then Th(M) is NTP2. We also generalize this result to obtain that, if M is a bounded PRC or PpC field with exactly n orders or p-adic valuations respectively, then Th(M) is strong of burden n. This also allows us to explicitly compute the burden of types, and to describe forking. Other results of independent interest are some amalgamation results, and the elimination of imaginaries for bounded PRC fields. Keywords: Model theory, ordered fields, p-adic valuation, real closed fields, p-adically closed fields, PRC, PpC, NIP, NTP2, elimination of imaginaries
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RÉMY, Bertrand. "Sur les propriétés algébriques et géométriques des groupes de Kac-Moody." Habilitation à diriger des recherches, 2003. http://tel.archives-ouvertes.fr/tel-00007119.
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Ce mémoire présente un point de vue issu de la théorie des groupes discrets sur les groupes de Kac-Moody. Sur les corps finis, ces groupes sont de type fini ; ils opèrent sur de nouveaux immeubles jouissant bien souvent de remarquables propriétés de courbure négative. On justifie que les groupes de Kac-Moody de type fini peuvent être vus comme des généralisations de certains groupes $S$-arithmétiques en caractéristique positive. On explique comment ils fournissent de nouveaux immeubles, et pourquoi on peut s'attendre à ce que les groupes eux-mêmes soient nouveaux. Nous considérons aussi des groupes totalement discontinus généralisant certains groupes semi-simples sur des corps locaux, comme en attestent leurs propriétés combinatoires fines et leur simplicité topologique. L'étude de leurs frontières de Furstenberg est évoquée. Nous résumons la preuve de la complète non linéarité de certains groupes de Kac-Moody. C'est ici que nous utilisons les propriétés des groupes topologiques précédents, en les combinant à un théorème de super-rigidité du commensurateur. En fait, on peut construire des groupes dont toutes les images linéaires sont finies, quel que soit le corps de base à l'arrivée. Enfin, nous conjecturons divers résultats sur les groupes précédemment définis, par exemple, la non linéarité (et peut-être la simplicité) d'une vaste classe de groupes de Kac-Moody de présentation finie. Nous conjecturons également la simplicité abstraite des groupes de Kac-Moody géométriquement complétés, et proposons un lien entre ces groupes et une autre définition des groupes de Kac-Moody (issue de l'étude des variétés de Schubert et de la théorie des représentations). Nous relions ces conjectures à des travaux en cours sur les compactifications d'immeubles de Bruhat-Tits.
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BRISUDOVÁ, Eva. "Rozvoj myšlenkových a komunikačních dovedností dětí předškolního věku v kontextu Filozofie pro děti." Master's thesis, 2018. http://www.nusl.cz/ntk/nusl-385118.
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The diploma thesis consists of theoretical and practical part. The theoretical part deals with a definition of important concepts such as philosophy for children, historical development of this program, personality of a child, communication and thinking of pre-school children. The practical part is conceived as a controlled dialogue with children in preschool education, with a great emphasis on expressing their emotions and experiencing a given situation.