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Sibirskii Matematicheskii Zhurnal, 2013, Volume 54, Number 1, Pages 131–149 (Mi smj2407)  

This article is cited in 4 scientific papers (total in 4 papers)

Lie algebras admitting a metacyclic frobenius group of automorphisms

N. Yu. Makarenko, E. I. Khukhro

Sobolev Institute of Mathematics, Novosibirsk, Russia
Full-text PDF (378 kB) Citations (4)
References:
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.
Keywords: Frobenius groups, automorphism, Lie algebras, nilpotency class.
Received: 31.10.2012
English version:
Siberian Mathematical Journal, 2013, Volume 54, Issue 1, Pages 99–113
DOI: https://doi.org/10.1134/S0037446613010138
Bibliographic databases:
Document Type: Article
UDC: 512.5
Language: Russian
Citation: N. Yu. Makarenko, E. I. Khukhro, “Lie algebras admitting a metacyclic frobenius group of automorphisms”, Sibirsk. Mat. Zh., 54:1 (2013), 131–149; Siberian Math. J., 54:1 (2013), 99–113
Citation in format AMSBIB
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\paper Lie algebras admitting a~metacyclic frobenius group of automorphisms
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\pages 131--149
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\jour Siberian Math. J.
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\pages 99--113
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  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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