Abstract
Assume that a Lie type algebra admits a Frobenius group of automorphisms with cyclic kernel \( F \) of order \( n \) and complement \( H \) of order \( q \) such that the fixed-point subalgebra with respect to \( F \) is trivial and the fixed-point subalgebra with respect to \( H \) is nilpotent of class \( c \). If the ground field contains a primitive \( n \)th root of unity, then the algebra is nilpotent and the nilpotency class is bounded in terms of \( q \) and \( c \). The result extends the well-known theorem of Khukhro, Makarenko, and Shumyatsky on Lie algebras with metacyclic Frobenius group of automorphisms.
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Acknowledgments
The author is grateful to the referee for the careful reading of the paper and for a number of valuable comments that helped to improve the manuscript.
Funding
The study was supported by the Russian Science Foundation grant no. 21–11–00286, https://rscf.ru/project/ 21-11-00286.
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Translated from Sibirskii Matematicheskii Zhurnal, 2023, Vol. 64, No. 3, pp. 598–610. https://doi.org/10.33048/smzh.2023.64.312
Dedicated to V.D. Mazurov on the occasion of his 80th birthday.
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Makarenko, N.Y. Nilpotency of Lie Type Algebras with Metacyclic Frobenius Groups of Automorphisms. Sib Math J 64, 639–648 (2023). https://doi.org/10.1134/S0037446623030126
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DOI: https://doi.org/10.1134/S0037446623030126