Finite Groups of Bounded Rank with an Almost Regular Automorphism of Prime Order

被引：0
作者：
E. I. Khukhro
机构：
[1] Sobolev Institute of Mathematics,
来源：
Siberian Mathematical Journal | 2002年 / 43卷
关键词：
finite group; rank; automorphism; almost regular; powerful ; -group; Lie ring; nilpotent;
D O I：
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摘要：
We prove that if a finite group G of rank r admits an automorphism ϕ of prime order having exactly m fixed points, then G has a ϕ-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).
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页码：955 / 962
页数：7
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