Groups with bounded centralizer chains and the Borovik–Khukhro conjecture-Reference-Cited by-同舟云学术

Groups with bounded centralizer chains and the Borovik–Khukhro conjecture

Published:2018-07-14 Issue:6 Volume:21 Page:1095-1110
ISSN:1435-4446
Container-title:Journal of Group Theory
language:en
Short-container-title:

Author:

Buturlakin Alexander A.¹,Revin Danila O.¹,Vasil’ev Andrey V.¹

Affiliation:

1. Sobolev Institute of Mathematics , 4 Acad. Koptyug avenue , Novosibirsk 630090 , Russia; and Novosibirsk State University, 1, Pirogova str., Novosibirsk 630090 , Russia

Abstract

Abstract Let G be a locally finite group and let F ⁢ ( G )

{F(G)}

be the Hirsch–Plotkin radical of G. Let S denote the full inverse image of the generalized Fitting subgroup of G / F ⁢ ( G )

{G/F(G)}

in G. Assume that there is a number k such that the length of every nested chain of centralizers in G does not exceed k. The Borovik–Khukhro conjecture states, in particular, that under this assumption, the quotient G / S

{G/S}

contains an abelian subgroup of finite index bounded in terms of k. We disprove this statement and prove a weak analogue of it.

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

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