Littérature scientifique sur le sujet « Locally nilpotent »

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Articles de revues sur le sujet "Locally nilpotent"

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HAVAS, GEORGE, et M. R. VAUGHAN-LEE. « 4-ENGEL GROUPS ARE LOCALLY NILPOTENT ». International Journal of Algebra and Computation 15, no 04 (août 2005) : 649–82. http://dx.doi.org/10.1142/s0218196705002475.

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Questions about nilpotency of groups satisfying Engel conditions have been considered since 1936, when Zorn proved that finite Engel groups are nilpotent. We prove that 4-Engel groups are locally nilpotent. Our proof makes substantial use of both hand and machine calculations.
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Burns, R. G., et Yuri Medvedev. « Group Laws Implying Virtual Nilpotence ». Journal of the Australian Mathematical Society 74, no 3 (juin 2003) : 295–312. http://dx.doi.org/10.1017/s1446788700003335.

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AbstractIf ω ≡ 1 is a group law implying virtual nilpotence in every finitely generated metabelian group satisfying it, then it implies virtual nilpotence for the finitely generated groups of a large class of groups including all residually or locally soluble-or-finite groups. In fact the groups of satisfying such a law are all nilpotent-by-finite exponent where the nilpotency class and exponent in question are both bounded above in terms of the length of ω alone. This yields a dichotomy for words. Finally, if the law ω ≡ 1 satisfies a certain additional condition—obtaining in particular for any monoidal or Engel law—then the conclusion extends to the much larger class consisting of all ‘locally graded’ groups.
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Wehrfritz, B. A. F. « Some nilpotent and locally nilpotent matrix groups ». Journal of Pure and Applied Algebra 60, no 3 (octobre 1989) : 289–312. http://dx.doi.org/10.1016/0022-4049(89)90089-3.

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TRAUSTASON, GUNNAR. « A NOTE ON THE LOCAL NILPOTENCE OF 4-ENGEL GROUPS ». International Journal of Algebra and Computation 15, no 04 (août 2005) : 757–64. http://dx.doi.org/10.1142/s021819670500244x.

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Recently Havas and Vaughan-Lee proved that 4-Engel groups are locally nilpotent. Their proof relies on the fact that a certain 4-Engel group T is nilpotent and this they prove using a computer and the Knuth–Bendix algorithm. In this paper we give a short handproof of the nilpotency of T.
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Liao, Jun, et Yanjun Liu. « Minimal Non-nilpotent and Locally Nilpotent Fusion Systems ». Algebra Colloquium 23, no 03 (20 juin 2016) : 455–62. http://dx.doi.org/10.1142/s1005386716000432.

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The main purpose of this note is to show that there is a one-to-one correspondence between minimal non-nilpotent (resp., locally nilpotent) saturated fusion systems and finite p′-core-free p-constrained minimal non-nilpotent (resp., locally p-nilpotent) groups.
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Detinko, A. S., et D. L. Flannery. « Locally Nilpotent Linear Groups ». Irish Mathematical Society Bulletin 0056 (2005) : 37–51. http://dx.doi.org/10.33232/bims.0056.37.51.

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Karaś, Marek. « Locally Nilpotent Monomial Derivations ». Bulletin of the Polish Academy of Sciences Mathematics 52, no 2 (2004) : 119–21. http://dx.doi.org/10.4064/ba52-2-2.

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SHUMYATSKY, PAVEL. « A (locally nilpotent)-by-nilpotent variety of groups ». Mathematical Proceedings of the Cambridge Philosophical Society 132, no 2 (mars 2002) : 193–96. http://dx.doi.org/10.1017/s0305004102005571.

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Longobardi, Patrizia, Mercede Maj, Howard Smith et James Wiegold. « Torsion-free groups isomorphic to all of their non-nilpotent subgroups ». Journal of the Australian Mathematical Society 71, no 3 (décembre 2001) : 339–48. http://dx.doi.org/10.1017/s1446788700002974.

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AbstractThe main result is that every torsion-free locally nilpotent group that is isomorphic to each of its nonnilpotent subgroups is nilpotent, that is, a torsion-free locally nilpotent group G that is not nilpotent has a non-nilpotent subgroup H that is not isomorphic to G.
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TRAUSTASON, GUNNAR. « TWO GENERATOR 4-ENGEL GROUPS ». International Journal of Algebra and Computation 15, no 02 (avril 2005) : 309–16. http://dx.doi.org/10.1142/s0218196705002189.

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Using known results on 4-Engel groups one can see that a 4-Engel group is locally nilpotent if and only if all its 3-generator subgroups are nilpotent. As a step towards settling the question whether all 4-Engel groups are locally nilpotent we show that all 2-generator 4-Engel groups are nilpotent.
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Thèses sur le sujet "Locally nilpotent"

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Wang, Zhiqing. « Locally nilpotent derivations of polynomial rings ». Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape9/PQDD_0018/NQ48119.pdf.

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Milian, Dagmara. « Locally nilpotent 5-Engel p-groups ». Thesis, University of Oxford, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.561122.

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In this thesis we investigate the structure of locally nilpotent 5-Engel p-groups. We show that for p > 7, locally nilpotent 5-Engel p-groups have class at most 10. This is a global theorem, where the result is not dependent on the number of generators of the group. The proof uses new and established Lie methods and a custom C++ implementation of an algorithm that constructs minimal generating sets and structure constants of multi- graded Lie algebras in a variety defined by three multilinear relations, which hold in the Lie rings associated with 5-Engel p-groups. We obtain our results by calculating in the set Q(p) = {~ I x E Z, yE Z+, Y # 0 modulo any p f/. p} (where p is a set of excluded primes and x, y are arbitrarily large integers), as well as the fields Zp, p prime. We introduce several reduction theorems, making the result possible. We also present results about the normal closure of elements in these groups. We use a Higman reduction theorem and the same custom C++ program to show that locally nilpotent 5-Engel p-groups, p 2: 5, are Fitting, with Fitting degree at most 4 if p > 7, at most 5 if p = 7 and at most 6 if p = 5. These results are best possible.
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Chitayat, Michael. « Locally Nilpotent Derivations and Their Quasi-Extensions ». Thesis, Université d'Ottawa / University of Ottawa, 2016. http://hdl.handle.net/10393/35072.

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In this thesis, we introduce the theory of locally nilpotent derivations and use it to compute certain ring invariants. We prove some results about quasi-extensions of derivations and use them to show that certain rings are non-rigid. Our main result states that if k is a field of characteristic zero, C is an affine k-domain and B = C[T,Y] / < T^nY - f(T) >, where n >= 2 and f(T) \in C[T] is such that delta^2(f(0)) != 0 for all nonzero locally nilpotent derivations delta of C, then ML(B) != k. This shows in particular that the ring B is not a polynomial ring over k.
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Khoury, Joseph. « Locally nilpotent derivations and their rings of constants ». Thesis, University of Ottawa (Canada), 2001. http://hdl.handle.net/10393/9028.

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Given a UFD R containing Q , we study R-elementary derivations of B = R[Y1,..., Ym], i.e., R-derivations satisfying D( Yi) ∈ R for all i; in the particular case of m = 3, we will show that if R is a polynomial ring in n variables over a field k (of characteristic zero), and a1, a3, a3 ∈ R are three monomials, then the kernel of the derivation i=13ai6 /6Yi of B is generated over R by at most three linear elements in the Yi's. This gives a partial answer to a question of A. van den Essen ([27]) about the existence of elementary derivations in dimension six whose kernels are not finitely generated. A set of generators is given for the kernel of R-elementary fixed point free derivations of B. Also, some interesting examples of elementary derivations in dimensions six and seven are provided as well as a criterion for a derivation of R[2] (i.e., a polynomial ring in two variables over R) to be R-elementary. Given a field k of characteristic zero, it is well-known that the kernel of any linear derivation of k[X 1,..., Xn] (that is, a k-derivation which maps each Xi to a linear form in X1,..., Xn) is a finitely generated k-algebra (see [28]). All known proofs of this result are non-constructive in the sense that we do not know a generating set for the kernel. Nowicki conjectured in [25] that the kernel of the derivation d = i=1nXi6 /6Yi of k[X1,..., Xn, Y1,..., Yn] is generated over k by the elements uij = XiYj - XjYi for 1 ≤ i ≤ j ≤ n. Using the theory of Groebner bases, we prove this conjecture in the more general case of the derivation D = i=1nXti i6/6Yi where each ti is a nonnegative integer. Note that in the case of the derivation D, the finite generation of the kernel is no longer evident. Note also that the generators of ker D are linear in the Yi's over k[X1,..., Xn]; we will show that this is not always the case for elementary derivations by giving an example of an elementary derivation in dimension seven whose kernel is finitely generated but cannot be generated by linear forms.
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EL, Houari Hassan. « Algorithms for locally nilpotent derivations in dimension two and three ». Limoges, 2007. https://aurore.unilim.fr/theses/nxfile/default/7d0e7c9d-8bec-4ccf-af81-92abce4349cb/blobholder:0/2007LIMO4049.pdf.

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Les dérivations localement nilpotentes sur les anneaux des polynômes sont des objets de grande importance dans beaucoup de domaines de mathématiques. Durant la dernière décennie, elles ont connu un véritable progrès et sont devenues un élément essentiel pour la compréhension de la géométrie algébrique affine et d’algèbre commutative. Cette importance est due au fait que certains problèmes classiques dans ces domaines, telles que la conjecture jacobienne, le problème d’élimination, le problème de plongement et le problème de linéarisation, ont été reformulés dans la théorie des dérivations localement nilpotentes. Cette thèse porte sur l’étude algorithmique des problèmes liés aux dérivations localement nilpotentes et leurs applications aux auto-morphismes polynomiaux de l’espace affine. Elle a pour objectif de présenter, d’une part, quelques problèmes dans lesquels les dérivations localement nilpotentes jouent un rôle crucial, à savoir le problème des coordonnées et le problème de paramétrisation polynomial des courbes algébriques dans l’espace affine. Et d’autre part, de donner quelques algorithmes qui peuvent contribuer à la compréhension des dérivations localement nilpotente en dimension trois, à savoir les algorithmes du rang et de triangulabilité des dérivations localement nilpotentes
Derivations, especially locally nilpotent ones, over polynomial rings are objects of great importance in many fields of pure and applied mathematics. Nowadays, locally nilpotent derivations have made remarkable progress and became an important topic in understanding affine algebraic geometry and commutative algebra. This is due to the fact that some classic problems in these areas, such as the Jacobian conjecture, the Linearization problem and the Cancellation problem, can be reformulated in terms of locally nilpotent derivations. This thesis is about the algorithmic study of problems linked to locally nilpotent derivations and their applications to the study of polynomial automorphisms of the affine space. Its aim is to present, on one hand, some problems in which locally nilpotent derivations play a crucial role, namely, the coordinate problem and the parametrization problem. On the other hand, give some algorithms concerning locally nilpotent derivations, which may contribute in understanding locally nilpotent derivations in three dimensional case, namely, rang and triangulability algorithms of locally nilpotent derivations
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Nur, Alexandra. « Locally Nilpotent Derivations and the Cancellation Problem in Affine Algebraic Geometry ». Thesis, University of Ottawa (Canada), 2011. http://hdl.handle.net/10393/28926.

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Let K be a field of characteristic zero and let R [n] denote the polynomial ring in n variables over a ring R for any n ∈ N , n > 0. We present some basic theory for the study of locally nilpotent derivations as an effective tool in algebraic geometry. Using this tool, we examine the Cancellation Problem in affine algebraic geometry, which asks: Let A be a K -algebra such that A[1] = K [n+1]. Does it follow that A = K [n]? This problem is open for n > 2. We present the solutions to the cases n = 1 and n = 2, in the latter case essentially following the algebraic method of Crachiola and Makar-Limanov [9]. We examine a potential counterexample, R = K [X, Y, Z, T]/⟨X + X ²Y + Z² + T³⟩, referred to as Russell's Cubic. We show that while R closely resembles a polynomial ring in 3 variables, we have that R ≠ K&sqbl0;3&sqbr0; , a result due to Makar-Limanov [25]. This is achieved by showing that the Derksen invariant of R is not equal to the Derksen invariant of K&sqbl0;3&sqbr0; . It is unknown if R[1] is a polynomial ring in 4 variables over K , nonetheless, we examine some properties of R [1] which highlight its similarities with K&sqbl0;4&sqbr0; .
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Nyobe, Likeng Samuel Aristide. « Locally Nilpotent Derivations on Polynomial Rings in Two Variables over a Field of Characteristic Zero ». Thesis, Université d'Ottawa / University of Ottawa, 2017. http://hdl.handle.net/10393/35906.

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The main goal of this thesis is to present the theory of Locally Nilpotent Derivations and to show how it can be used to investigate the structure of the polynomial ring in two variables k[X;Y] over a field k of characteristic zero. The thesis gives a com- plete proof of Rentschler's Theorem, which describes all locally nilpotent derivations of k[X;Y]. Then we present Rentschler's proof of Jung's Theorem, which partially describes the group of automorphisms of k[X;Y]. Finally, we present the proof of the Structure Theorem for the group of automorphisms of k[X;Y].
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Merighe, Liliam Carsava. « Uma introdução às derivações localmente nilpotentes com uma aplicação ao 14º problema de Hilbert ». Universidade de São Paulo, 2015. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-05082015-102547/.

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O principal objetivo desta dissertação é estudar um contraexemplo para o Décimo Quarto Problema de Hilbert no caso de dimensão n = 5, que foi apresentado por Arno van den Essen ([6]) em 2006 e que é baseado em um contraexemplo de D. Daigle e G. Freudenburg ([4]). Para isso, serão estudados os conceitos fundamentais da teoria de derivações e os princípios básicos das derivações localmente nilpotentes, bem como seus respectivos corolários. Dentre esses princípios encontra-se o Princípio 13, que garante que, se B é uma k- álgebra polinomial, digamos B = k[x1; ..., xn], (onde k é um corpo de característica zero) e D é uma derivação localmente nilpotente sobre B, então seu núcleo A = ker D satisfaz A = B &cap: Frac(A). Assim encontramos o contraexemplo esperado, ao mostrar que A não é finitamente gerado sobre k. Além disso, no apêndice deste trabalho, é dada uma prova para o caso de dimensão 1 do Décimo Quarto Problema de Hilbert.
The main objective of this thesis is to study a counterexample to the Hilberts Fourteenth Problem in dimension n = 5, which was presented by Arno van den Essen ([6]) in 2006 and that is based on a counterexample of D. Daigle and G. Freudenburg ([4]). For these purpose, we study the fundamental concepts of the theory of derivations and the basic principles of locally nilpotent derivations and their corollaries. Among these principles, Principle 13 ensures that if B is a k-algebra polynomial, say B = k[x1; ..., xn], (where k is a field of characteristic zero) and D is a locally nilpotent derivation on B, then its kernel A = ker D satisfies A = B ∩ Frac(A). Once we have proved that A is not finitely generated over k, we find the expected counterexample. In addition, in the appendix of this work is given a proof for the Hilberts Fourteenth Problemin dimension n = 1.
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Abreu, Kelyane Barboza de. « Derivações localmente nilpotentes e os teoremas de Rentschler e Jung ». Universidade Federal da Paraí­ba, 2014. http://tede.biblioteca.ufpb.br:8080/handle/tede/7438.

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The main goal of this work is to furnish a proof of the well-known Rentschler s Theorem, which describes the structure of the locally nilpotent derivations on the polynomial ring in two indeterminates (over a field of characteristic zero), up to conjugation by tame automorphisms. As a central application of this result, we prove Jung s Theorem, concerning the generators of the group of automorphisms in two variables. Finally, some examples are discussed, illustrating connections to other important topics.
O principal objetivo deste trabalho é fornecer uma demonstração do bem-conhecido Teorema de Rentschler, que descreve a estrutura das derivações localmente nilpotentes sobre o anel de polinômios em duas variáveis (sobre um corpo de característica zero), a menos de conjugação por automorfismos tame . Como aplicação central deste resultado, provamos o Teorema de Jung, sobre os geradores do grupo de automorfismos em duas variáveis. Finalmente, alguns exemplos são discutidos, ilustrando conexões com outros tópicos importantes.
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丸橋, 広和. « 単連結べき零Lie群のパラメータ剛性をもつ作用 ». 京都大学 (Kyoto University), 2014. http://hdl.handle.net/2433/188455.

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Livres sur le sujet "Locally nilpotent"

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Freudenburg, Gene. Algebraic Theory of Locally Nilpotent Derivations. Berlin, Heidelberg : Springer Berlin Heidelberg, 2017. http://dx.doi.org/10.1007/978-3-662-55350-3.

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Freudenburg, Gene. Algebraic Theory of Locally Nilpotent Derivations. Springer London, Limited, 2006.

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Algebraic Theory of Locally Nilpotent Derivations. Berlin, Heidelberg : Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/978-3-540-29523-5.

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Freudenburg, Gene. Algebraic Theory of Locally Nilpotent Derivations. Springer, 2018.

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Freudenburg, Gene. Algebraic Theory of Locally Nilpotent Derivations. Springer, 2017.

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Freudenburg, Gene. Algebraic Theory of Locally Nilpotent Derivations. Springer, 2010.

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Algebraic Theory of Locally Nilpotent Derivations (Encyclopaedia of Mathematical Sciences). Springer, 2006.

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Chapitres de livres sur le sujet "Locally nilpotent"

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Daigle, Daniel. « Locally Nilpotent Sets of Derivations ». Dans Polynomial Rings and Affine Algebraic Geometry, 41–71. Cham : Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-42136-6_2.

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Makar-Limanov, L. « Locally nilpotent derivations of affine domains ». Dans CRM Proceedings and Lecture Notes, 221–29. Providence, Rhode Island : American Mathematical Society, 2011. http://dx.doi.org/10.1090/crmp/054/12.

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Freudenburg, Gene. « First Principles ». Dans Algebraic Theory of Locally Nilpotent Derivations, 1–39. Berlin, Heidelberg : Springer Berlin Heidelberg, 2017. http://dx.doi.org/10.1007/978-3-662-55350-3_1.

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Freudenburg, Gene. « Slices, Embeddings and Cancellation ». Dans Algebraic Theory of Locally Nilpotent Derivations, 265–85. Berlin, Heidelberg : Springer Berlin Heidelberg, 2017. http://dx.doi.org/10.1007/978-3-662-55350-3_10.

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Freudenburg, Gene. « Epilogue ». Dans Algebraic Theory of Locally Nilpotent Derivations, 287–98. Berlin, Heidelberg : Springer Berlin Heidelberg, 2017. http://dx.doi.org/10.1007/978-3-662-55350-3_11.

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Freudenburg, Gene. « Further Properties of LNDs ». Dans Algebraic Theory of Locally Nilpotent Derivations, 41–72. Berlin, Heidelberg : Springer Berlin Heidelberg, 2017. http://dx.doi.org/10.1007/978-3-662-55350-3_2.

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Freudenburg, Gene. « Polynomial Rings ». Dans Algebraic Theory of Locally Nilpotent Derivations, 73–112. Berlin, Heidelberg : Springer Berlin Heidelberg, 2017. http://dx.doi.org/10.1007/978-3-662-55350-3_3.

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Freudenburg, Gene. « Dimension Two ». Dans Algebraic Theory of Locally Nilpotent Derivations, 113–36. Berlin, Heidelberg : Springer Berlin Heidelberg, 2017. http://dx.doi.org/10.1007/978-3-662-55350-3_4.

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Freudenburg, Gene. « Dimension Three ». Dans Algebraic Theory of Locally Nilpotent Derivations, 137–65. Berlin, Heidelberg : Springer Berlin Heidelberg, 2017. http://dx.doi.org/10.1007/978-3-662-55350-3_5.

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Freudenburg, Gene. « Linear Actions of Unipotent Groups ». Dans Algebraic Theory of Locally Nilpotent Derivations, 167–91. Berlin, Heidelberg : Springer Berlin Heidelberg, 2017. http://dx.doi.org/10.1007/978-3-662-55350-3_6.

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Actes de conférences sur le sujet "Locally nilpotent"

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CLARK, JOHN. « LOCALLY SEMI-T-NILPOTENT FAMILIES OF MODULES ». Dans Proceedings of the 4th China-Japan-Korea International Conference. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812701671_0005.

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TRABELSI, NADIR. « LOCALLY GRADED GROUPS WITH FEW NON-(TORSION-BY-NILPOTENT) SUBGROUPS ». Dans Proceedings of a Conference in Honor of Akbar Rhemtulla. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812708670_0022.

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