scholarly journals Groups in which every non-nilpotent subgroup is self-normalizing

2017 ◽  
Vol 15 (1) ◽  
pp. 39-51
Author(s):  
Costantino Delizia ◽  
Urban Jezernik ◽  
Primož Moravec ◽  
Chiara Nicotera
Keyword(s):  
Nilpotent Subgroup

scholarly journals Compact groups with a set of positive Haar measure satisfying a nilpotent law

2021 ◽  
pp. 1-4
Author(s):  
ALIREZA ABDOLLAHI ◽  
MEISAM SOLEIMANI MALEKAN
Keyword(s):  
Compact Group ◽  
Haar Measure ◽  
Positive Answer ◽  
Nilpotent Subgroup ◽  
Compact Groups

Abstract The following question is proposed by Martino, Tointon, Valiunas and Ventura in [4, question 1·20]: Let G be a compact group, and suppose that \[\mathcal{N}_k(G) = \{(x_1,\dots,x_{k+1}) \in G^{k+1} \;|\; [x_1,\dots, x_{k+1}] = 1\}\] has positive Haar measure in $G^{k+1}$ . Does G have an open k-step nilpotent subgroup? We give a positive answer for $k = 2$ .

On homotopy nilpotency

2021 ◽  
Vol 56 (2) ◽  
pp. 391-406
Author(s):  
Marek Golasiński ◽  
Keyword(s):  
Lie Group ◽  
Nilpotent Subgroup ◽  
Compact Lie Group ◽  
Loop Spaces

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.

scholarly journals On Mp-embedded primary subgroups of finite groups

2016 ◽  
Vol 53 (4) ◽  
pp. 429-439
Author(s):  
Jia Zhang ◽  
Long Miao
Keyword(s):  
Finite Groups ◽  
Nilpotent Subgroup ◽  
Primary Subgroups

A subgroup H of G is called Mp-embedded in G, if there exists a p-nilpotent subgroup B of G such that Hp ∈ Sylp(B) and B is Mp-supplemented in G. In this paper, we use Mp-embedded subgroups to study the structure of finite groups.

scholarly journals On nilpotent automorphism groups of function fields

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Nurdagül Anbar ◽  
Burçin Güneş
Keyword(s):  
Automorphism Group ◽  
Function Field ◽  
Automorphism Groups ◽  
Function Fields ◽  
Infinite Family ◽  
Nilpotent Subgroup ◽  
Closed Field ◽  
Algebraically Closed Field

Abstract We study the automorphisms of a function field of genus g ≥ 2 over an algebraically closed field of characteristic p > 0. More precisely, we show that the order of a nilpotent subgroup G of its automorphism group is bounded by 16 (g – 1) when G is not a p-group. We show that if |G| = 16(g – 1), then g – 1 is a power of 2. Furthermore, we provide an infinite family of function fields attaining the bound.

scholarly journals Locally graded groups with a nilpotency condition on infinite subsets

2000 ◽  
Vol 69 (3) ◽  
pp. 415-420 ◽  
Author(s):  
Costantino Delizia ◽  
Akbar Rhemtulla ◽  
Howard Smith
Keyword(s):  
Positive Integer ◽  
Infinite Subset ◽  
Nilpotent Subgroup ◽  
Finitely Generated ◽  
Finite Image ◽  
Nontrivial Subgroup ◽  
Locally Graded Groups

AbstractA group G is locally graded if every finitely generated nontrivial subgroup of G has a nontrivial finite image. Let N (2, k)* denote the class of groups in which every infinite subset contains a pair of elements that generate a nilpotent subgroup of class at most k. We show that if G is a finitely generated locally graded N (2, k)*-group, then there is a positive integer c depending only on k such that G/Zc (G) is finite.

scholarly journals ON THE EXPONENT OF A VERBAL SUBGROUP IN A FINITE GROUP

2012 ◽  
Vol 93 (3) ◽  
pp. 325-332 ◽  
Author(s):  
PAVEL SHUMYATSKY
Keyword(s):  
Finite Group ◽  
Positive Integer ◽  
Nilpotent Subgroup ◽  
Multilinear Commutator ◽  
Verbal Subgroup ◽  
A Finite Group ◽  
Commutator Word

AbstractLet $w$ be a multilinear commutator word. We prove that if $e$ is a positive integer and $G$ is a finite group in which any nilpotent subgroup generated by $w$-values has exponent dividing $e$, then the exponent of the corresponding verbal subgroup $w(G)$ is bounded in terms of $e$ and $w$only.

HYPERCENTRAL GROUPS WITH ALL SUBGROUPS SUBNORMAL III

2001 ◽  
Vol 33 (5) ◽  
pp. 591-598 ◽  
Author(s):  
HOWARD SMITH
Keyword(s):  
Nilpotent Subgroup ◽  
Hypercentral Group

It is shown that a hypercentral group that has all subgroups subnormal and every non-nilpotent subgroup of bounded defect is nilpotent. As a consequence, a hypercentral group of length at most ω in which every subgroup is subnormal is nilpotent.

scholarly journals Nilpotent groups are not dualizable

2002 ◽  
Vol 72 (2) ◽  
pp. 173-180 ◽  
Author(s):  
R. Quackenbush ◽  
C. S. Szabó
Keyword(s):  
Finite Group ◽  
Abelian Group ◽  
Abelian Groups ◽  
Finite Abelian Group ◽  
Nilpotent Groups ◽  
Nilpotent Subgroup ◽  
Pontryagin Duality ◽  
Sylow Subgroups ◽  
Companion Article

AbstractIt is shown that no finite group containing a non-abelian nilpotent subgroup is dualizable. This is in contrast to the known result that every finite abelian group is dualizable (as part of the Pontryagin duality for all abelian groups) and to the result of the authors in a companion article that every finite group with cyclic Sylow subgroups is dualizable.

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