Makarenko, N. Y. and Khukhro, Evgeny (2013) Lie algebras admitting a metacyclic Frobenius group of automorphisms. Siberian Mathematical Journal, 54 (1). pp. 99113. ISSN 00374466
Full content URL: http://link.springer.com/article/10.1134%2FS003744...
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Item Type:  Article 

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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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