## 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 |
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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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