On solubility of groups with bounded centralizer chains

Khukhro, E. I. (2009) On solubility of groups with bounded centralizer chains. Glasgow Math. J., 51. pp. 49-54.

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Abstract

The $c$-dimension of a group is the maximum length of a chain of nested centralizers. It is proved that a periodic locally soluble group of finite $c$-dimension $k$ is soluble of derived length bounded in terms of~$k$, and the rank of its quotient by the Hirsch--Plotkin radical is bounded in terms of~$k$. Corollary: a pseudo-(finite soluble) group of finite $c$-dimension $k$ is soluble of derived length bounded in terms of~$k$.

Item Type: Article
Uncontrolled Keywords: centralizer lattice; derived length; pseudofinite groups
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 20 Group theory and generalizations
Depositing User: Professor Evgeny Khukhro
Date Deposited: 18 Oct 2012
Last Modified: 20 Oct 2017 14:13
URI: https://eprints.maths.manchester.ac.uk/id/eprint/1892

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