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 |
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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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