Locally finite groups with all subgroups either subnormal or nilpotent-by-Chernikov
Open Mathematics, 2012 Abstract Let G be a locally finite group satisfying the condition given in the title and suppose that G is not nilpotent-by-Chernikov. It is shown that G has a section S that is not nilpotent-by-Chernikov, where S is either a p-group or a semi-direct product of the additive group A of a locally finite field F by a subgroup K of the ...
Cutolo Giovanni, Smith Howard
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Locally finite groups containing a 2 -element with Chernikov centralizer [PDF]
, 2014 Suppose that a locally finite group G has a 2-element g with Chernikov centralizer. It is proved that if the involution in ⟨g⟩ has nilpotent centralizer, then G has a soluble subgroup of finite ...
A Turull +19 more
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On pairs of antagonistic subgroups and theirs influence on the structure of groups [PDF]
, 2023 In this survey we collect some results on the influence on the structure of a group of some families of its subgroups satisfying conditions related to normality.
Kurdachenko, Leonid A. +3 more
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The nilpotency of some groups with all subgroups subnormal [PDF]
, 1998 Let G be a group with all subgroups subnormal. A normal subgroup N of G is said to be G-minimax if it has a ¯nite G-invariant series whose factors are abelian and satisfy either max-G or min- G. It is proved that if the normal closure of every element of
Kurdachenko, L. A., Smith, H.
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Pronormality, contranormality and generalized nilpotency in infinite groups [PDF]
, 2003 This article is dedicated to some criteria of generalized nilpotency involving pronormality and abnormality.
Kurdachenko, Leonid A. +1 more
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A class of generalized supersoluble groups [PDF]
, 2005 This paper is devoted to the study of groups G in the universe cL of all radical locally finite groups with min-p for all primes p such that every [delta]-chief factor of G is either a cyclic group of prime order or a quasicyclic group.
Ballester-Bolinches, Adolfo +1 more
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Locally nilpotent linear groups with the weak chain conditions on subgroups of infinite central dimension [PDF]
, 2008 Let V be a vector space over a field F. If G≤GL(V, F), the central dimension of G is the F-dimension of the vector space V/CV (G). In [DEK] and [KS], soluble linear groups in which the set Licd(G) of all proper infinite central dimensional subgroups of G
Kurdachenko, Leonid A. +2 more
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Finite groups and Lie rings with an automorphism of order 2n [PDF]
, 2017 . Suppose that a finite group G admits an automorphism ϕ of order 2n such that the fixed-point subgroup CG (ϕ2n−1) of the involution ϕ2n−1 is nilpotent of class c. Let m = |CG (ϕ)| be the number of fixed points of ϕ.
Khukhro, E. I. +2 more
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Locally finite p-groups with all subgroups either subnormal or nilpotent-by-Chernikov [PDF]
International Journal of Group Theory, 2012 We pursue further our investigation, begun in [H.~Smith, Groups with all subgroups subnormal or nilpotent-by-{C}hernikov, emph{Rend. Sem. Mat. Univ. Padova} 126 (2011), 245--253] and continued in [G.~Cutolo and H.~Smith, Locally finite groups with all ...
H. Smith, G. Cutolo
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On the fixed-point set of an automorphism of a group [PDF]
, 2013 Let Ø be an automorphism of a group G. Under variousfiniteness or solubility hypotheses, for example under polycyclicity, the commutator subgroup [G; Ø] has finite index in G if thefixed-point set CG(Ø) of Ø in G isfinite, but not conversely, even for ...
Wehrfritz, B. A. F.
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