Lie algebras admitting a metacyclic frobenius group of automorphisms

被引：0
作者：
N. Yu. Makarenko
E. I. Khukhro
机构：
[1] Sobolev Institute of Mathematics,
来源：
Siberian Mathematical Journal | 2013年 / 54卷
关键词：
Frobenius groups; automorphism; Lie algebras; nilpotency class;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Suppose that a Lie algebra L admits a finite Frobenius group of automorphisms FH with cyclic kernel F and complement H such that the characteristic of the ground field does not divide |H|. It is proved that if the subalgebra CL(F) of fixed points of the kernel has finite dimension m and the subalgebra CL(H) of fixed points of the complement is nilpotent of class c, then L has a nilpotent subalgebra of finite codimension bounded in terms of m, c, |H|, and |F| whose nilpotency class is bounded in terms of only |H| and c. Examples show that the condition of F being cyclic is essential.
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页码：99 / 113
页数：14
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