Fixed points of the complements of Frobenius groups of automorphisms

Khukhro, Evgeny (2010) Fixed points of the complements of Frobenius groups of automorphisms. Siberian Mathematical Journal, 51 (3). pp. 552-556. ISSN 0037-4466

Full content URL: http://link.springer.com/article/10.1007%2Fs11202-...

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Fixed points of the complements of Frobenius groups of automorphisms

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Abstract

Suppose that a finite group G admits a Frobenius group of automorphisms BA with kernel B and complement A. It is proved that if N is a BA-invariant normal subgroup of G such that (|N|, |B|) = 1 and C N (B) = 1 then C G/N (A) = C G (A)N/N. If N = G is a nilpotent group then we give as a corollary some description of the fixed points C L(G)(A) in the associated Lie ring L(G) in terms of C G (A). In particular, this applies to the case where GB is a Frobenius group as well (so that GBA is a 2-Frobenius group, with not necessarily coprime orders of G and A).

Additional Information:Translation of the Russian journal: Sibirskii Matematicheskii Zhurnal
Keywords:Frobenius group, Automorphism, Nilpotent group, Associated Lie ring
Subjects:G Mathematical and Computer Sciences > G100 Mathematics
Divisions:College of Science > School of Mathematics and Physics
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ID Code:15588
Deposited On:29 Oct 2014 11:55

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