Lie algebras admitting a metacyclic frobenius group of automorphisms |
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Authors: | N Yu Makarenko E I Khukhro |
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Institution: | 11013. Sobolev Institute of Mathematics, Novosibirsk, Russia
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Abstract: | 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 L (F) of fixed points of the kernel has finite dimension m and the subalgebra C L (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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