Khukhro, E. I.
(2002)
*Finite groups of bounded rank with an almost regular automorphism of prime order.*
Siberian Mathematical Journal, 43
(5).
pp. 955-962.
ISSN 0037-4466

Full content URL: http://dx.doi.org/10.1023/A:1020171227191

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Item Type: | Article |
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Item Status: | Live Archive |

## Abstract

We prove that if a finite group G of rank r admits an automorphism Ï� of prime order having exactly m fixed points, then G has a Ï�-invariant subgroup of (r,m)-bounded index which is nilpotent of r-bounded class (Theorem 1). Thus, for automorphisms of prime order the previous results of Shalev, Khukhro, and Jaikin-Zapirain are strengthened. The proof rests, in particular, on a result about regular automorphisms of Lie rings (Theorem 3). The general case reduces modulo available results to the case of finite p-groups. For reduction to Lie rings powerful p-groups are also used. For them a useful fact is proved which allows us to "glue together" nilpotency classes of factors of certain normal series (Theorem 2).

Keywords: | Algebra |
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Subjects: | G Mathematical and Computer Sciences > G100 Mathematics |

Divisions: | College of Science > School of Mathematics and Physics |

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ID Code: | 15738 |

Deposited On: | 19 Nov 2014 15:45 |

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