Lie algebras admitting a metacyclic Frobenius group of automorphisms

Makarenko, N. Y. and Khukhro, Evgeny (2013) Lie algebras admitting a metacyclic Frobenius group of automorphisms. Siberian Mathematical Journal, 54 (1). pp. 99-113. ISSN 0037-4466

Full content URL: http://link.springer.com/article/10.1134%2FS003744...

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Lie algebras admitting a metacyclic Frobenius group of automorphisms

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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 CL(F) of fixed points of the kernel has finite dimension m and the subalgebra CL(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. © 2013 Pleiades Publishing, Ltd.

Additional Information:Translation of the Russian journal: Sibirskii Matematicheskii Zhurnal.
Keywords:Automorphism, Frobenius group, Lie algebras, Nilpotency class
Subjects:G Mathematical and Computer Sciences > G110 Pure Mathematics
Divisions:College of Science > School of Mathematics and Physics
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ID Code:15579
Deposited On:28 Oct 2014 10:40

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