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Journal articles on the topic 'Nilpotente'

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Published: 10 March 2023

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1

Chaudouard, Pierre-Henri, and Gérard Laumon. "SUR LE COMPTAGE DES FIBRÉS DE HITCHIN NILPOTENTS." Journal of the Institute of Mathematics of Jussieu 15, no. 1 (August 7, 2014): 91–164. http://dx.doi.org/10.1017/s1474748014000292.

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Cet article est une contribution à la fois au calcul du nombre de fibrés de Hitchin sur une courbe projective et à l’explicitation de la partie nilpotente de la formule des traces d’Arthur-Selberg pour une fonction test très simple. Le lien entre les deux questions a été établi dans [Chaudouard, Sur le comptage des fibrés de Hitchin. À paraître aux actes de la conférence en l’honneur de Gérard Laumon]. On décompose cette partie nilpotente en une somme d’intégrales adéliques indexées par les orbites nilpotentes. Pour les orbites de type «régulières par blocs», on explicite complètement ces intégrales en termes de la fonction zêta de la courbe.

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2

Dettmann, Beate. "Schwach Nilpotente Gruppen." Results in Mathematics 19, no. 1-2 (March 1991): 54–56. http://dx.doi.org/10.1007/bf03322415.

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3

Von Walcher, S. "Über homogene nilpotente Polynome." Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 56, no. 1 (December 1986): 153–55. http://dx.doi.org/10.1007/bf02941513.

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4

Fidelis, Marcello, and José Roger de Oliveira Gomes. "Uma abordagem elementar para uma descrição do subgrupo de Fitting e do radical solúvel de um grupo finito G." REMAT: Revista Eletrônica da Matemática 7, no. 2 (December 15, 2021): e3005. http://dx.doi.org/10.35819/remat2021v7i2id5193.

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Este trabalho apresenta uma abordagem que prioriza o uso dos Teoremas do Isomorfismo de Grupos para estudar os grupos solúveis e os grupos nilpotentes com vistas a descrever o radical solúvel S(G) como o maior subgrupo normal solúvel do grupo finito G e o subgrupo de Fitting F(G) como o maior subgrupo normal nilpotente de um grupo finito G. Como aplicação, mostramos que esta descrição nos permite verificar que S(G) e F(G) são exemplos de uma classe de subgrupos definida em Deaconescu e Walls (2011) para os quais vale uma generalização de um resultado clássico que relaciona um grupo G com seu grupo de automorfismos Aut(G).

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5

Tani, Gabriella Corsi. "p-gruppi finiti con automorfo nilpotente." Rendiconti del Seminario Matematico e Fisico di Milano 58, no. 1 (December 1988): 55–66. http://dx.doi.org/10.1007/bf02925230.

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6

Michel, Horst. "Nilpotente Endomorphismen von freien abelschen Gruppen." Publicationes Mathematicae Debrecen 18, no. 1-4 (July 1, 2022): 261–72. http://dx.doi.org/10.5486/pmd.1971.18.1-4.29.

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7

Von Jantzen, J. C. "Kohomologie vonp-Lie-Algebren und nilpotente Elemente." Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 56, no. 1 (December 1986): 191–219. http://dx.doi.org/10.1007/bf02941516.

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8

Félix, Yves, and Jean-Claude Thomas. "Le tor differentiel d'une fibration non nilpotente." Journal of Pure and Applied Algebra 38, no. 2-3 (November 1985): 217–33. http://dx.doi.org/10.1016/0022-4049(85)90010-6.

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9

Golasiński, Marek. "On homotopy nilpotency." Glasnik Matematicki 56, no. 2 (December 23, 2021): 391–406. http://dx.doi.org/10.3336/gm.56.2.10.

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We review established and recent results on the homotopy nilpotence of spaces. In particular, the homotopy nilpotency of the loop spaces \(\Omega(G/K)\) of homogenous spaces \(G/K\) for a compact Lie group \(G\) and its closed homotopy nilpotent subgroup \(K \lt G\) is discussed.

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10

Fanaï, Hamid-Reza. "Sur un type particulier de valeur propre des solvariétés d'Einstein." Bulletin of the Australian Mathematical Society 68, no. 1 (August 2003): 39–43. http://dx.doi.org/10.1017/s0004972700037394.

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On montre que la partie nilpotente d'une solveriété d'Einstein standard, dont le type de valeur propre est égal à (1 < 2; d1, d2), est nécessairement indécomposable si d1 et d2 sont premiers entre eux.

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11

Sabourin, Hervé. "Sur la structure transverse à une orbite nilpotente adjointe." Canadian Journal of Mathematics 57, no. 4 (August 1, 2005): 750–70. http://dx.doi.org/10.4153/cjm-2005-030-4.

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AbstractWe are interested in Poisson structures transverse to nilpotent adjoint orbits in a complex semi-simple Lie algebra, and we study their polynomial nature. Furthermore, in the case of sln, we construct some families of nilpotent orbits with quadratic transverse structures.

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12

Bonnet, Pierre. "Paramétrisation du dual d'une algèbre de Lie nilpotente." Annales de l’institut Fourier 38, no. 3 (1988): 169–97. http://dx.doi.org/10.5802/aif.1144.

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13

Jiang, Donghua. "Un 3-polyGEM de cohomologie modulo 2 nilpotente." Annales de l’institut Fourier 54, no. 4 (2004): 1053–72. http://dx.doi.org/10.5802/aif.2043.

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14

Burns, R. G., and Yuri Medvedev. "Group Laws Implying Virtual Nilpotence." Journal of the Australian Mathematical Society 74, no. 3 (June 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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15

Arnal, Didier. "Le produit star de Kontsevich sur le dual d'une algèbre de Lie nilpotente." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 327, no. 9 (November 1998): 823–26. http://dx.doi.org/10.1016/s0764-4442(99)80112-8.

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16

Lannes, Jean, and Lionel Schwartz. "Sur Les Groupes D’Homotopie Des Espaces Dont La Cohomologie Modulo 2 Est Nilpotente." Israel Journal of Mathematics 66, no. 1-3 (December 1989): 260–73. http://dx.doi.org/10.1007/bf02765897.

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17

Csörgő, Piroska. "A characterization of nilpotent Moufang loops of odd order." Journal of Algebra and Its Applications 15, no. 10 (November 24, 2016): 1650183. http://dx.doi.org/10.1142/s0219498816501838.

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Glauberman and Wright in [G. G. Glauberman and C. R. B. Wright, Nilpotence of finite Moufang 2-loops, J. Algebra 8 (1968) 415–417] proved that a nilpotent Moufang loop is the direct product of [Formula: see text]-loops for some primes [Formula: see text], consequently the elements of coprime order commute in a nilpotent Moufang loop. In this paper, we prove that in Moufang loops of odd order this condition is equivalent to the central nilpotence.

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18

Zhukovskaya, Zukhra Tagirovna, and Sergey Evgenyevich Zhukovskiy. "ON EQUATIONS GENERATED BY NONLINEAR NILPOTENT MAPPINGS." Tambov University Reports. Series: Natural and Technical Sciences, no. 124 (2018): 637–42. http://dx.doi.org/10.20310/1810-0198-2018-23-124-637-642.

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A generalization of a nilpotent linear operator concept is proposed for nonlinear mapping acting from R^2 to R^2. The properties of nonlinear nilpotent mappings are investigated. Criterions of nilpotence for differentiable and polynomial mappings are obtained.

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19

Bulois, Michaël. "Composantes irréductibles de la variété commutante nilpotente d’une algèbre de Lie symétrique semi-simple." Annales de l’institut Fourier 59, no. 1 (2009): 37–80. http://dx.doi.org/10.5802/aif.2426.

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20

Sullivan, R. P. "Nilpotents in semigroups of partial transformations." Bulletin of the Australian Mathematical Society 55, no. 3 (June 1997): 453–67. http://dx.doi.org/10.1017/s0004972700034092.

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In 1987, Sullivan determined when a partial transformation α of an infinite set X can be written as a product of nilpotent transformations of the same set: he showed that when this is possible and the cardinal of X is regular then α is a product of 3 or fewer nilpotents with index at most 3. Here, we show that 3 is best possible on both counts, consider the corresponding question when the cardinal of X is singular, and investigate the role of nilpotents with index 2. We also prove that the nilpotent-generated semigroup is idempotent-generated but not conversely.

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21

Mostovoy, Jacob, José M. Pérez-Izquierdo, and Ivan P. Shestakov. "On torsion-free nilpotent loops." Quarterly Journal of Mathematics 70, no. 3 (May 31, 2019): 1091–104. http://dx.doi.org/10.1093/qmath/haz010.

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Abstract We show that a torsion-free nilpotent loop (that is, a loop nilpotent with respect to the dimension filtration) has a torsion-free nilpotent left multiplication group of, at most, the same class. We also prove that a free loop is residually torsion-free nilpotent and that the same holds for any free commutative loop. Although this last result is much stronger than the usual residual nilpotence of the free loop proved by Higman, it is established, essentially, by the same method.

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22

TIAN, JIANJUN PAUL, and YI MING ZOU. "FINITELY GENERATED NIL BUT NOT NILPOTENT EVOLUTION ALGEBRAS." Journal of Algebra and Its Applications 13, no. 01 (August 20, 2013): 1350070. http://dx.doi.org/10.1142/s0219498813500709.

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To use evolution algebras to model population dynamics that both allow extinction and introduction of certain gametes in finite generations, nilpotency must be built into the algebraic structures of these algebras with the entire algebras not to be nilpotent if the populations are assumed to evolve for a long period of time. To adequately address this need, evolution algebras over rings with nilpotent elements must be considered instead of evolution algebras over fields. This paper develops some criteria, which are computational in nature, about the nilpotency of these algebras, and shows how to construct finitely generated evolution algebras which are nil but not nilpotent.

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23

Kelarev, A. V., and J. Okniński. "On group graded rings satisfying polynomial identities." Glasgow Mathematical Journal 37, no. 2 (May 1995): 205–10. http://dx.doi.org/10.1017/s0017089500031104.

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A number of classical theorems of ring theory deal with nilness and nilpotency of the Jacobson radical of various ring constructions (see [10], [18]). Several interesting results of this sort have appeared in the literature recently. In particular, it was proved in [1] that the Jacobson radical of every finitely generated PI-ring is nilpotent. For every commutative semigroup ring RS, it was shown in [11] that if J(R) is nil then J(RS) is nil. This result was generalized to all semigroup algebras satisfying polynomial identities in [15] (see [16, Chapter 21]). Further, it was proved in [12] that, for every normal band B, if J(R) is nilpotent, then J(RB) is nilpotent. A similar result for special band-graded rings was established in [13, Section 6]. Analogous theorems concerning nilpotency and local nilpotency were proved in [2] for rings graded by finite and locally finite semigroups.

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24

MARGOLIS, S., M. SAPIR, and P. WEIL. "CLOSED SUBGROUPS IN PRO-V TOPOLOGIES AND THE EXTENSION PROBLEM FOR INVERSE AUTOMATA." International Journal of Algebra and Computation 11, no. 04 (August 2001): 405–45. http://dx.doi.org/10.1142/s0218196701000498.

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We relate the problem of computing the closure of a finitely generated subgroup of the free group in the pro-V topology, where V is a pseudovariety of finite groups, with an extension problem for inverse automata which can be stated as follows: given partial one-to-one maps on a finite set, can they be extended into permutations generating a group in V? The two problems are equivalent when V is extension-closed. Turning to practical computations, we modify Ribes and Zalesskiĭ's algorithm to compute the pro-p closure of a finitely generated subgroup of the free group in polynomial time, and to effectively compute its pro-nilpotent closure. Finally, we apply our results to a problem in finite monoid theory, the membership problem in pseudovarieties of inverse monoids which are Mal'cev products of semilattices and a pseudovariety of groups. Résumé: Nous établissons un lien entre le problème du calcul de l'adhéerence d'un sous-groupe finiment engendré du groupe libre dans la topologie pro-V, oú V est une pseudovariété de groupes finis, et un probléme d'extension pour les automates inversifs qui peut être énoncé de la faç con suivante: étant données des transformations partielles injectives d'un ensemble fini, peuvent-elles être étendues en des permutations qui engendrent un groupe dans V? Les deux problèmes sont équivalents si V est fermée par extensions. Nous intéressant ensuite aux calculs pratiques, nous modifions l'algorithme de Ribes et Zalesskiĭ pour calculer l'adhérence pro-p d'un sous-groupe finiment engendré du groupe libre en temps polynomial et pour calculer effectivement sa clôture pro-nilpotente. Enfin nous appliquons nos résultats à un problème de théorie des monoïdes finis, celui de de l'appartenance dans les pseudovariétés de monoïdes inversifs qui sont des produits de Mal'cev de demi-treillis et d'une pseudovariété de groupes.

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25

Wei, Huaquan, and Yanming Wang. "THE $c$-SUPPLEMENTED PROPERTY OF FINITE GROUPS." Proceedings of the Edinburgh Mathematical Society 50, no. 2 (May 17, 2007): 493–508. http://dx.doi.org/10.1017/s0013091504001385.

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AbstractThe purpose of this paper is to study the influence of $c$-supplemented minimal subgroups on the $p$-nilpotency of finite groups. We obtain ‘iff' and ‘localized' versions of theorems of Itô and Buckley on nilpotence, $p$-nilpotence and supersolvability.

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26

Detinko, A. S., and D. L. Flannery. "Computing in Nilpotent Matrix Groups." LMS Journal of Computation and Mathematics 9 (2006): 104–34. http://dx.doi.org/10.1112/s1461157000001212.

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AbstractWe present algorithms for testing nilpotency of matrix groups over finite fields, and for deciding irreducibility and primitivity of nilpotent matrix groups. The algorithms also construct modules and imprimitivity systems for nilpotent groups. In order to justify our algorithms, we prove several structural results for nilpotent linear groups, and computational and theoretical results for abstract nil-potent groups, which are of independent interest.

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27

HAVAS, GEORGE, and M. R. VAUGHAN-LEE. "4-ENGEL GROUPS ARE LOCALLY NILPOTENT." International Journal of Algebra and Computation 15, no. 04 (August 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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28

Goswami, Nabanita, and Helen K. Saikia. "On nilpotency of the right singular ideal of semiring." Boletim da Sociedade Paranaense de Matemática 37, no. 2 (April 23, 2017): 123–27. http://dx.doi.org/10.5269/bspm.v37i2.34308.

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We introduce the concept of nilpotency of the right singular ideal of a semiring. We discuss some properties of such nilpotency and singular ideals. We show that the right singular ideal of a semiring with a.c.c. for right annihilators, is nilpotent.

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29

Benoist, Yves. "Modules simples sur une algèbre de Lie nilpotente contenant un vecteur propre pour une sous-algèbre." Annales scientifiques de l'École normale supérieure 23, no. 3 (1990): 495–517. http://dx.doi.org/10.24033/asens.1609.

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30

Shi, Jiangtao, Klavdija Kutnar, and Cui Zhang. "A Note on Special Local 2-Nilpotent Groups and the Solvability of Finite Groups." Algebra Colloquium 25, no. 04 (December 2018): 541–46. http://dx.doi.org/10.1142/s1005386718000378.

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A finite group G is called a special local 2-nilpotent group if G is not 2-nilpotent, the Sylow 2-subgroup P of G has a section isomorphic to the quaternion group of order 8, [Formula: see text] and NG(P) is 2-nilpotent. In this paper, it is shown that SL2(q), [Formula: see text], is a special local 2-nilpotent group if and only if [Formula: see text], and that GL2(q), [Formula: see text], is a special local 2-nilpotent group if and only if q is odd. Moreover, the solvability of finite groups is also investigated by giving two generalizations of a result from [A note on p-nilpotence and solvability of finite groups, J. Algebra 321 (2009) 1555–1560].

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31

TRAUSTASON, GUNNAR. "A NOTE ON THE LOCAL NILPOTENCE OF 4-ENGEL GROUPS." International Journal of Algebra and Computation 15, no. 04 (August 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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32

Ganjali, Masoumeh, Ahmad Erfanian, and Intan Muchtadi-Alamsyah. "Finite p-groups which are non-inner nilpotent." MATHEMATICA 64 (87), no. 1 (April 15, 2022): 75–82. http://dx.doi.org/10.24193/mathcluj.2022.1.09.

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A group G is called a non-inner nilpotent group, whenever it is nilpotent with respect to a non-inner automorphism. In 2018, all finitely generated abelian non-inner nilpotent groups have been classified. Actually, the authors proved that a finitely generated abelian group G is a non-inner nilpotent group, if G is not isomorphic to cyclic groups Z_p_1p_2...p_t and Z, for a positive integer t and distinct primes p_1, p_2,..., p_t. We conjecture that all finite non-abelian p-groups are non-inner nilpotent and we prove this conjecture for finite $p$-groups of nilpotency class 2 or of co-class 2.

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33

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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34

Riley, D. M., and A. Shalev. "Restricted Lie Algebras and Their Envelopes." Canadian Journal of Mathematics 47, no. 1 (February 1, 1995): 146–64. http://dx.doi.org/10.4153/cjm-1995-008-7.

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AbstractLet L be a restricted Lie algebra over a field of characteristic p. Denote by u(L) its restricted enveloping algebra and by ωu(L) the augmentation ideal of u(L). We give an explicit description for the dimension subalgebras of L, namely those ideals of L defined by Dn(L) - L∩ωu(L)n for each n ≥ 1. Using this expression we describe the nilpotence index of ωU(L). We also give a precise characterisation of those L for which ωu(L) is a residually nilpotent ideal. In this case we show that the minimal number of elements required to generate an arbitrary ideal of u(L) is finitely bounded if and only if L contains a 1-generated restricted subalgebra of finite codimension. Subsequently we examine certain analogous aspects of the Lie structure of u(L). In particular we characterise L for which u(L) is residually nilpotent when considered as a Lie algebra, and give a formula for the Lie nilpotence index of u(L). This formula is then used to describe the nilpotence class of the group of units of u(L).

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35

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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36

Bhatt, Suchi, Harish Chandra, and Meena Sahai. "Group algebras of Lie nilpotency index 14." Asian-European Journal of Mathematics 13, no. 05 (April 4, 2019): 2050088. http://dx.doi.org/10.1142/s1793557120500886.

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Let [Formula: see text] be a group and let [Formula: see text] be a field of characteristic [Formula: see text]. Lie nilpotent group algebras of strong Lie nilpotency index at most 13 have been classified by many authors. In this paper, our aim is to classify the group algebras [Formula: see text] which are strongly Lie nilpotent of index 14.

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37

Garaialde Ocaña, Oihana, and Jon González-Sánchez. "Transporting cohomology in Lazard correspondence." Journal of Algebra and Its Applications 16, no. 06 (April 12, 2017): 1750119. http://dx.doi.org/10.1142/s0219498817501195.

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Lazard correspondence provides an isomorphism of categories between finitely generated nilpotent pro-[Formula: see text] groups of nilpotency class smaller than [Formula: see text] and finitely generated nilpotent [Formula: see text]-Lie algebras of nilpotency class smaller than [Formula: see text]. Denote by [Formula: see text] and [Formula: see text] the group cohomology functors and the Lie cohomology functors respectively. The aim of this paper is to show that for [Formula: see text], [Formula: see text] and [Formula: see text], and for a given category of modules the cohomology functors [Formula: see text] and [Formula: see text] are naturally equivalent. A similar result is proved for [Formula: see text] with the relative cohomology groups.

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38

Amberg, Bernhard, Silvana Franciosi, and Francesco de Giovanni. "Groups with a nilpotent triple factorisation." Bulletin of the Australian Mathematical Society 37, no. 1 (February 1988): 69–79. http://dx.doi.org/10.1017/s0004972700004159.

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In the investigation of factorised groups one often encounters groups G = AB = AK = BK which have a triple factorisation as a product of two subgroups A and B and a normal subgroup K of G. It is of particular interest to know whether G satisfies some nilpotency requirement whenever the three subgroups A, B and K satisfy this same nilpotency requirement. A positive answer to this problem for the classes of nilpotent, hypercentral and locally nilpotent groups is given under the hypothesis that K is a minimax group or G has finite abelian section rank. The results become false if K has only finite Prüfer rank. Some applications of the main theorems are pointed out.

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39

JESPERS, ERIC, and DAVID RILEY. "NILPOTENT LINEAR SEMIGROUPS." International Journal of Algebra and Computation 16, no. 01 (February 2006): 141–60. http://dx.doi.org/10.1142/s0218196706002913.

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We characterize the structure of linear semigroups satisfying certain global and local nilpotence conditions and deduce various Engel-type results. For example, using a form of Zel'manov's solution of the restricted Burnside problem we are able to show that a finitely generated residually finite group is nilpotent if and only if it satisfies a certain 4-generator property of semigroups we call WMN. Methods of linear semigroups then allow us to prove that a linear semigroup is Mal'cev nilpotent precisely when it satisfies WMN. As an application, we show that a finitely generated associative algebra is nilpotent when viewed as a Lie algebra if and only if its adjoint semigroup is WMN.

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40

Kleinfeld, Erwin, and Harry F. Smith. "Right alternative algebras with commutators in a nucleus." Bulletin of the Australian Mathematical Society 46, no. 1 (August 1992): 81–90. http://dx.doi.org/10.1017/s0004972700011692.

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Let A be a right alternative algebra, and [A, A] be the linear span of all commutators in A. If [A, A] is contained in the left nucleus of A, then left nilpotence implies nilpotence. If [A, A] is contained in the right nucleus, then over a commutative-associative ring with 1/2, right nilpotence implies nilpotence. If [A, A] is contained in the alternative nucleus, then the following structure results hold: (1) If A is prime with characteristic ≠ 2, then A is either alternative or strongly (–1, 1). (2) If A is a finite-dimensional nil algebra, over a field of characteristic ≠ 2, then A is nilpotent. (3) Let the algebra A be finite-dimensional over a field of characteristic ≠ 2, 3. If A/K is separable, where K is the nil radical of A, then A has a Wedderburn decomposition

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41

Kim, Goansu, and C. Y. Tang. "On the Residual Finiteness of Polygonal Products of Nilpotent Groups." Canadian Mathematical Bulletin 35, no. 3 (September 1, 1992): 390–99. http://dx.doi.org/10.4153/cmb-1992-052-8.

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AbstractIn general polygonal products of finitely generated torsion-free nilpotent groups amalgamating cyclic subgroups need not be residually finite. In this paper we prove that polygonal products of finitely generated torsion-free nilpotent groups amalgamating maximal cyclic subgroups such that the amalgamated cycles generate an isolated subgroup in the vertex group containing them, are residually finite. We also prove that, for finitely generated torsion-free nilpotent groups, if the subgroups generated by the amalgamated cycles have the same nilpotency classes as their respective vertex groups, then their polygonal product is residually finite.

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42

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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43

Kudryavtseva, Ganna, and Volodymyr Mazorchuk. "On the Semigroup of Square Matrices." Algebra Colloquium 15, no. 01 (March 2008): 33–52. http://dx.doi.org/10.1142/s1005386708000047.

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We study the structure of nilpotent subsemigroups in the semigroup M(n,𝔽) of all n×n matrices over a field 𝔽 with respect to the operation of the usual matrix multiplication. We describe the maximal subsemigroups among the nilpotent subsemigroups of a fixed nilpotency degree and classify them up to isomorphism. We also describe isolated and completely isolated subsemigroups and conjugated elements in M(n,𝔽).

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44

Macdonald, Gordon W. "Distance From Projections to Nilpotents." Canadian Journal of Mathematics 47, no. 4 (August 1, 1995): 841–51. http://dx.doi.org/10.4153/cjm-1995-043-3.

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AbstractThe distance from an arbitrary rank-one projection to the set of nilpotent operators, in the space of k × k matrices with the usual operator norm, is shown to be sec(π/(k:+2))/2. This gives improved bounds for the distance between the set of all non-zero projections and the set of nilpotents in the space of k × k matrices. Another result of note is that the shortest distance between the set of non-zero projections and the set of nilpotents in the space of k × k matrices is .

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45

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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46

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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47

Bhatt, Suchi, and Harish Chandra. "A note on modular group algebras with upper Lie nilpotency indices." Algebra and Discrete Mathematics 33, no. 2 (2022): 1–20. http://dx.doi.org/10.12958/adm1694.

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Let KG be the modular group algebra of anarbitrary group G over a field K of characteristic p>0. In thispaper we give some improvements of upper Lie nilpotency indext L(KG) of the group algebra KG. It can be seen that if KG is Lie nilpotent, then its lower as well as upper Lie nilpotency index is atleast p+1. In this way the classification of group algebras KG with next upper Lie nilpotency indext L(KG) up to 9p−7 have alreadybeen classified. Furthermore, we give a complete classification ofmodular group algebraKGfor which the upper Lie nilpotency index is 10p−8.

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48

Mukhamedov, Farrukh, Otabek Khakimov, Bakhrom Omirov, and Izzat Qaralleh. "Derivations and automorphisms of nilpotent evolution algebras with maximal nilindex." Journal of Algebra and Its Applications 18, no. 12 (November 3, 2019): 1950233. http://dx.doi.org/10.1142/s0219498819502335.

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This paper is devoted to the nilpotent finite-dimensional evolution algebras [Formula: see text] with [Formula: see text]. We describe the Lie algebra of derivations of these algebras. Moreover, in terms of these Lie algebras, we fully construct nilpotent evolution algebra with maximal index of nilpotency. Furthermore, this result allowed us fully characterize all local and 2-local derivations of the considered evolution algebras. Besides, all automorphisms and local automorphisms of these algebras are found.

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49

Marques-Smith, M. Paula O., and R. P. Sullivan. "Nilpotents and congruences on semigroups of transformations with fixed rank." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 125, no. 2 (1995): 399–412. http://dx.doi.org/10.1017/s0308210500028092.

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In 1988, Howie and Marques-Smith studied Pm, a Rees quotient semigroup of transformations associated with a regular cardinal m, and described the elements which can be written as a product of nilpotents in Pm. In 1981, Marques proved that if Δm denotes the Malcev congruence on Pm, then Pm/Δm is congruence-free for any infinite m. In this paper, we describe the products of nilpotents in Pm when m is nonregular, and determine all the congruences on Pm when m is an arbitrary infinite cardinal. We also investigate when a nilpotent is a product of idempotents.

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50

CAMACHO, L. M., J. M. CASAS, J. R. GÓMEZ, M. LADRA, and B. A. OMIROV. "ON NILPOTENT LEIBNIZ n-ALGEBRAS." Journal of Algebra and Its Applications 11, no. 03 (May 24, 2012): 1250062. http://dx.doi.org/10.1142/s0219498812500624.

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We study the nilpotency of Leibniz n-algebras related with the adapted version of Engel's theorem to Leibniz n-algebras. We also deal with the characterization of finite-dimensional nilpotent complex Leibniz n-algebras.

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