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 Lie algebras admitting a metacyclic Frobenius group of automorphisms


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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 $C LF$ of fixed points of the kernel has finite dimension $m$ and the subalgebra $C LH$ 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 the kernel $F$ being cyclic is essential.



Author: N. Yu. Makarenko; E. I. Khukhro

Source: https://archive.org/







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