Finite groups of bounded rank with an almost regular automorphism of prime order

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
Item Status:Live Archive

Abstract

We prove that if a finite group G of rank r admits an automorphism � of prime order having exactly m fixed points, then G has a �-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
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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