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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To Victor Danilovich Mazurov on the occasion of his 70th birthday.
Original Russian Text Copyright © 2013 Makarenko N.Yu. and Khukhro E.I.
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 54, No. 1, pp. 131–149, January–February, 2013.
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Makarenko, N.Y., Khukhro, E.I. Lie algebras admitting a metacyclic frobenius group of automorphisms. Sib Math J 54, 99–113 (2013). https://doi.org/10.1134/S0037446613010138
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DOI: https://doi.org/10.1134/S0037446613010138