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ON SOLUBILITY OF GROUPS WITH BOUNDED CENTRALIZER CHAINS

Published online by Cambridge University Press:  01 January 2009

E. I. KHUKHRO
E. I. KHUKHRO*
Affiliation:
Sobolev Institute of Mathematics, Novosibirsk 630090, Russia e-mail: khukhro@yahoo.co.uk
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Abstract

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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.

Keywords

Primary: 20D10Secondary: 03C2020D4520F1620F22
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 51 , Issue 1 , January 2009 , pp. 49 - 54
Copyright
Copyright © Glasgow Mathematical Journal Trust 2008

References

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