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arXiv · 2111.14649

Nilpotency of Lie type algebras with metacyclic Frobenius groups of automorphisms

N. Yu Makarenko
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Abstract

Suppose that a Lie type algebra L over a field K admits a Frobenius group of automorphisms FH with cyclic kernel F of order n and complement H such that the fixed-point subalgebra of F is trivial and the fixed-point subalgebra of H is nilpotent of class c. If the ground field K contains a primitive n-th root of unity, then L is nilpotent and the nilpotency class of L is bounded in terms of |H| and c. The result extends the known theorem of Khukhro, Makarenko and Shumyatsky on Lie algebras with metacyclic Frobenius group of automorphisms.

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N. Yu Makarenko. 2021-11-29. Nilpotency of Lie type algebras with metacyclic Frobenius groups of automorphisms. https://arxiv.org/abs/2111.14649

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