Khukhro, Evgeny (2010) Fixed points of the complements of Frobenius groups of automorphisms. Siberian Mathematical Journal, 51 (3). pp. 552556. ISSN 00374466
Full content URL: http://link.springer.com/article/10.1007%2Fs11202...
Documents 

PDF
__ddat02_staffhome_jpartridge_art%3A10.1007%2Fs1120201000579.pdf  Whole Document Restricted to Repository staff only 137kB 
Item Type:  Article 

Item Status:  Live Archive 
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 BAinvariant 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 2Frobenius 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 
Related URLs:  
ID Code:  15588 
Deposited On:  29 Oct 2014 11:55 
Repository Staff Only: item control page