This article is cited in 3 papers

Locally finite groups with bounded centralizer chains

A. A. Buturlakin^ab, A. V. Vasil'ev<sup>ab

a</sup> Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia
^b Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

Abstract: The $c$-dimension of a group $G$ is the maximal length of a chain of nested centralizers in $G$. We prove that a locally finite group of finite $c$-dimension $k$ has less than $5k$ non-Abelian composition factors.

Keywords: locally finite group, non-Abelian simple group, lattice of centralizers, $c$-dimension.

UDC: 512.544.5

Received: 29.10.2013

 English version: Algebra and Logic, 2013, 52:5, 367–370

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