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Relevant bibliographies by topics / Degree of nilpotence

Academic literature on the topic 'Degree of nilpotence'

Author: Grafiati

Published: 10 March 2023

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Journal articles on the topic "Degree of nilpotence"

1

Kireeva, Elena, and Vladimir Shchigolev. "The nilpotence degree of quantum Lie nilpotent algebras." International Journal of Algebra and Computation 28, no. 06 (September 2018): 1119–28. http://dx.doi.org/10.1142/s0218196718500492.

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We consider the quantum analog of the Lie commutator [Formula: see text] for an invertible element [Formula: see text] of the ground field and prove lower and upper bounds for the nilpotence degree of an associative algebra satisfying an identity of the form [Formula: see text].

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2

POWELL, GEOFFREY M. L. "The tensor product theorem for &∇tilde;-nilpotence and the dimension of unstable modules." Mathematical Proceedings of the Cambridge Philosophical Society 130, no. 3 (May 2001): 427–39. http://dx.doi.org/10.1017/s030500410100500x.

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Let [Fscr ] be the category of functors from the category of finite-dimensional [ ]2-vector spaces to [ ]2-vector spaces. The concept of &∇tilde;-nilpotence in the category [Fscr ] is used to define a ‘dimension’ for the category of analytic functors which has good properties. In particular, the paper shows that the tensor product F [otimes ] G of analytic functors which are respectively &∇tilde;s and &∇tilde;t nilpotent is &∇tilde;s+t − 1-nilpotent.The notion of &∇tilde;-nilpotence is extended to define a dimension in the category of unstable modules over the mod 2 Steenrod algebra, which is shown to coincide with the transcendence degree of an unstable Noetherian algebra over the Steenrod algebra.

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3

Croome, Sarah, and Mark L. Lewis. "𝑝-groups with exactly four codegrees." Journal of Group Theory 23, no. 6 (November 1, 2020): 1111–22. http://dx.doi.org/10.1515/jgth-2019-0073.

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AbstractLet G be a p-group, and let χ be an irreducible character of G. The codegree of χ is given by {\lvert G:\operatorname{ker}(\chi)\rvert/\chi(1)}. Du and Lewis have shown that a p-group with exactly three codegrees has nilpotence class at most 2. Here we investigate p-groups with exactly four codegrees. If, in addition to having exactly four codegrees, G has two irreducible character degrees, G has largest irreducible character degree {p^{2}}, {\lvert G:G^{\prime}\rvert=p^{2}}, or G has coclass at most 3, then G has nilpotence class at most 4. In the case of coclass at most 3, the order of G is bounded by {p^{7}}. With an additional hypothesis, we can extend this result to p-groups with four codegrees and coclass at most 6. In this case, the order of G is bounded by {p^{10}}.

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4

Minh, Pham Anh. "Any nilpotence degree occurs in mod-p cohomology rings of p-groups." Mathematische Zeitschrift 249, no. 2 (August 10, 2004): 387–400. http://dx.doi.org/10.1007/s00209-004-0703-7.

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5

ŁOPUSZAŃSKI, JAN. "A REMARK ON B.R.S. TRANSFORMATIONS." International Journal of Modern Physics A 03, no. 11 (November 1988): 2589–600. http://dx.doi.org/10.1142/s0217751x88001077.

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We scrutinize transformations constructed by taking the most general expressions consisting of terms of forms of the same degree in the fields A10, ν01, [Formula: see text], Q12 and F20 as well as operations d10 and s01, where the subscripts denote the degree of the forms in the x—and in the group parameter spaces. Imposing the requirement of nilpotence for d and s as well as Faddeev-Popov charge conservation we get a unique form of the B.R.S. transformation.

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6

Petrov, E. P. "On the degree of minimal identity of a finitely generated algebra with a fixed nilpotence index." Sibirskie Elektronnye Matematicheskie Izvestiya 16 (August 6, 2019): 1028–35. http://dx.doi.org/10.33048/semi.2019.16.071.

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7

Filho, Augusto Reynol. "Nilpotent Spaces: Some Inequalities on Nilpotency Degrees." Proceedings of the American Mathematical Society 115, no. 2 (June 1992): 501. http://dx.doi.org/10.2307/2159274.

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8

Reynol Filho, Augusto. "Nilpotent spaces: some inequalities on nilpotency degrees." Proceedings of the American Mathematical Society 115, no. 2 (February 1, 1992): 501. http://dx.doi.org/10.1090/s0002-9939-1992-1093597-8.

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9

PAJOOHESH, H., P. RODRIGUEZ, and C. WADDELL. "NILPOTENT INNER DERIVATIONS ON SOME SUBRINGS OF Mn(ℝ)." Journal of Algebra and Its Applications 12, no. 08 (July 31, 2013): 1350045. http://dx.doi.org/10.1142/s021949881350045x.

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It is known that the degree of nilpotency of a nilpotent derivation on a prime ring including the ring of n × n matrices must be an odd number. In this article we introduce subrings of the ring of of n × n matrices that admit derivations with an even degree of nilpotency.

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10

POURMAHMOOD-AGHABABA, HASAN. "APPROXIMATELY BIPROJECTIVE BANACH ALGEBRAS AND NILPOTENT IDEALS." Bulletin of the Australian Mathematical Society 87, no. 1 (May 22, 2012): 158–73. http://dx.doi.org/10.1017/s0004972712000251.

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AbstractBy introducing a new notion of approximate biprojectivity we show that nilpotent ideals in approximately amenable or pseudo-amenable Banach algebras, and nilpotent ideals with the nilpotency degree larger than two in biflat Banach algebras cannot have the special property which we call ‘property (𝔹)’ (Definition 5.2 below) and hence, as a consequence, they cannot be boundedly approximately complemented in those Banach algebras.

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Dissertations / Theses on the topic "Degree of nilpotence"

1

ELSHARIF, RAMADAN. "The Average of Some Irreducible Character Degrees." Kent State University / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=kent1616410634054592.

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2

Sanselme, Luc. "Algorithmes quantiques dans les groupes nilpotents." Paris 11, 2008. http://www.theses.fr/2008PA112297.

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Dans cette thèse, nous commençons par donner avec précision une définition formelle des groupes boîtes noires, et nous rappelons les principaux algorithmes existant dans ce cadre. Dans un deuxième temps, nous proposons une définition nouvelle d’un groupe boîte noire quantique. Nous formalisons, par ailleurs, précisément cette définition et donnons les principaux algorithmes quantiques connus dans ce cadre. Ensuite, nous donnons un certain nombre d’algorithmes de calcul de théorie algorithmique quantique des groupes dans les groupes résolubles, et dans certaines sous-classes particulières de ces groupes. Enfin, nous présentons un résultat original, démontré au cours de l’élaboration de cette thèse. Nous expliquons comment résoudre efficacement le problème du sous-groupe caché dans les groupes extraspéciaux et nilpotents de classe deux, en calcul quantique. Au passage, nous donnons un certain nombre de réductions du problème du sous-groupe caché, valable dans un groupe nilpotent de classe supérieure. Le dernier chapitre, un peu à part dans cette thèse, explique comment résoudre efficacement un système d’équations quadratiques dans un corps fini, résultat nécessaire pour résoudre le problème du sous-groupe caché dans les groupes nilpotents de classe 2
We start off this Ph. D. Thesis with giving the definition of a black-box group and reminding some algorithm associated with this group representation. Then, we put forward a new definition of a quantum black-box group. We explain precisely this new approach and we enumerate the main algorithms associated to this notion. After that, we give some algorithm of quantum computational group theory in solvable groups and in some subclasses of these solvable groups such as nilpotent groups, p-groups or extraspecial groups. Finally, we present a new result that was proved during this thesis. We show that we can solve efficiently, with a quantum computer, the hidden subgroup problem in extraspecial and nilpotent group of class 2. In addition, we give some reduction of the Hidden subgroup problem in nilpotent groups of higher classes. The last chapter of this thesis shows how to solve some system of quadratic equations over a finite field. This result is needed to solve the Hidden subgroup problem in nilpotent groups of class 2

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3

BENSALEM, NACEURDINE. "Localisation des courbes anormales et probleme d'accessibilite sur un groupe de lie hilbertien nilpotent de degre 2." Chambéry, 1998. http://www.theses.fr/1998CHAMS019.

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L'etude des chemins tangents a une distribution est motivee par de nombreux problemes variationnels, lies a des contraintes donnees par cette distribution. Contrairement a la situation sans contrainte, il existe dans ce cas, des chemins anormaux qui sont solutions du probleme variationnel, bien qu'il ne verifient pas les equations d'euler-lagrange associees. Le but de la premiere partie de cette these est d'etudier les chemins tangents a une distribution sur une variete hilbertienne. Lorsque la distribution est affine de hilbert-schmidt on obtient des resultats similaires au cas de la dimension finie. Le contexte central de notre travail est les groupes de lie hilbertiens nilpotents de degre 2. Ce cadre presente un interet par exemple en physique mathematique et plus particulierement dans l'etude des groupes de lacets sur un groupe de lie. Dans la deuxieme partie, on donne une caracterisation et une localisation des courbes anormales. Une application aux resultats obtenus est donnee sur les algebres de lie de type heisenberg generalise (hg). Ce type d'algebre joue un role important dans la theorie des champs en physique mathematique. Dans la troisieme partie nous avons etudie les problemes d'accessibilite sur un groupe de lie hilbertien nilpotent de degre 2 et nous avons etabli dans ce cadre un theoreme de chow. D'autres resultats complementaires ont ete obtenus, notamment, la demonstration d'un theoreme d'existence de solutions des systemes controles sur des varietes hilbertiennes et l'etude d'un probleme variationnel general en dimension infinie lie a des contraintes donnees par une distribution.

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Gomes, Manoel Messias de Ara?jo. "Strongly stable automorphisms of the categories of finitely generated free algebras of the varieties of all linear nilpotents algebras of degree 5." PROGRAMA DE P?S-GRADUA??O EM MATEM?TICA APLICADA E ESTAT?STICA, 2017. https://repositorio.ufrn.br/jspui/handle/123456789/24066.

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Este trabalho tem por objetivo o estudo dos automorfismos fortemente est?veis da categoria de todas as ?lgebras livres finitamente geradas na variedade de todas as ?lgebras Lineares Nilpotentes de grau 5. Apresentamos uma breve explica??o sobre o m?todo de opera??es verbais. Nosso interesse principal ? computar o grupo A/Y no caso da variedade de todas as ?lgebras lineares nilpotentes de grau 5. Tendo em vista que o estudo do grupo A/Y ? muito importante na ?rea de Geometria Alg?brica Universal, pois esse grupo nos d? as poss?veis diferen?as entre equival?ncia geom?trica e autom?rfica de ?lgebras.

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Gheri, Pietro. "Subnormalizers and p-elements in finite groups." Doctoral thesis, 2020. http://hdl.handle.net/2158/1193023.

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The probability that two elements of a finite group commute (i.e. generate an abelian subgroup), also known as the extit{degree of commutativity of G}, dc(G), is a well studied topic in group theory. A first result involving this probability is the theorem by Gustafson which states that the degree of commutativity of a finite nonabelian group is less than 5/8. As a natural generalization, one can consider the probability that two elements of a finite group generate a nilpotent subgroup, the degree of nilpotence. A Gustafson-like theorem for the degree of nilpotence was proved by Guralnick and Wilson in 2000 using the classification of finite simple groups: the degree of nilpotence of a finite nonnilpotent group is less than 1/2. We give a classification-free proof of this theorem. In our proof, an important role is played by the probability sp(G), i.e., the arithmetic mean of the ratios between |S_G(x)| and |G| where S_G(x) is the Wielandt's subnormalizer of x. The main result for our proof is a probabilistic version of Wielandt's criterion for subnormality, which depends on a formula for the order of subnormalizers of p-subgroups proved by Casolo. The analysis of the probability sp(G) leads to the following theorem: if G is a nonsolvable group then sp(G) <1/6. The proof of this theorem involves the classification of finite simple groups and takes up a large portion of the thesis. Inspired by a problem related to this theorem, the final chapter of the thesis is devoted to the investigation of the ratio between the number of p-elements and the order of a Sylow p-subgroup in a finite group. For a p-solvable group G we prove that this ratio is greater than the (p-1)/p th power of the number of Sylow p-subgroups of G. As for the non-p-solvable case, we state a conjecture that, if true, would imply the aforementioned bound for any finite group G and we provide a reduction of the conjecture to finite almost simple groups.

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Books on the topic "Degree of nilpotence"

1

The finite irreducible linear 2-groups of degree 4. Providence, R.I: American Mathematical Society, 1997.

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2

Nilpotent Structures in Ergodic Theory. American Mathematical Society, 2019.

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Conference papers on the topic "Degree of nilpotence"

1

Abd Manaf, Fadila Normahia, Nor Haniza Sarmin, Nor Muhainiah Mohd Ali, Ahmad Erfanian, and Mohammad Farrokhi Derakhshandeh Ghouchan. "A general case of the commutativity degree of nilpotent p-groups of class two." In PROCEEDINGS OF THE 20TH NATIONAL SYMPOSIUM ON MATHEMATICAL SCIENCES: Research in Mathematical Sciences: A Catalyst for Creativity and Innovation. AIP, 2013. http://dx.doi.org/10.1063/1.4801212.

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