Groups Which Are Dual to Layer-Finite

Kalashnikova, Nataliya; Kurdachenko, Leonid A.; Giovanni, Francesco de; Newell, Martin

doi:10.1515/9783110810387-010

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Proposition 33 Let G Be a Locally Soluble-by-®nite Group S1

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2010

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Cited by 3 publications

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“…Hence L is nilpotent by [1,Corollary 2.6]. This contradiction to the hypotheses shows that TaT n is ®nite for every n e N. By Corollary 6 of [4], P contains a normal divisible abelian subgroup W such that PaW is ®nite. Since P is nilpotent we have W ZP and the result follows.…”

Section: Proposition 33 Let G Be a Locally Soluble-by-®nite Group Smentioning

confidence: 93%

Groups with the maximum condition on non-nilpotent subgroups

Dixon¹,

Kurdachenko²

2001

Journal of Group Theory

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Section: Proposition 33 Let G Be a Locally Soluble-by-®nite Group Smentioning

confidence: 93%

Groups with the maximum condition on non-nilpotent subgroups

Dixon¹,

Kurdachenko²

2001

Journal of Group Theory

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Some Criteria for Existence of Supplements to Normal Subgroups and Their Applications

Kurdachenko

Otal

Subbotin

2010

Int. J. Algebra Comput.

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We established several new criteria for existence of complements and supplements to some normal abelian subgroups in groups. In passing, as one of the many useful applications and corollaries of these results, we obtained a description of some finitely generated soluble groups of finite Hirsch–Zaitsev rank. As another application of our results, we obtained a D.J.S. Robinson's theorem on structure of finitely generated soluble groups of finite section rank. The original proof of this theorem was homological, but all proofs in this paper, including this one, are purely group-theoretical.

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Locally nilpotent linear groups with the weak chain conditions on subgroups of infinite central dimension

Kurdachenko¹,

Escolano²,

Otal³

2008

Publicacions Matemàtiques

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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 /C V (G). In [DEK] and [KS], soluble linear groups in which the set L icd (G) of all proper infinite central dimensional subgroups of G satisfies the minimal condition and the maximal condition, respectively, have been described. On the other hand, in [MOS], periodic locally radical linear groups in which L icd (G) satisfies one of the weak chain conditions (the weak minimal condition or the weak maximal condition) have been characterized. In this paper, we begin the study of the non-periodic case by describing locally nilpotent linear groups in which L icd (G) satisfies one of the two weak chain conditions.

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Groups Which Are Dual to Layer-Finite

Cited by 3 publications

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Groups with the maximum condition on non-nilpotent subgroups

Groups with the maximum condition on non-nilpotent subgroups

Some Criteria for Existence of Supplements to Normal Subgroups and Their Applications

Locally nilpotent linear groups with the weak chain conditions on subgroups of infinite central dimension

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