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2012.92: On solubility of groups with bounded centralizer chains

2012.92: E. I. Khukhro (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 2000 > 20 Group theory and generalizations
MIMS number:2012.92
Deposited By:Professor Evgeny Khukhro
Deposited On:18 October 2012

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