Khukhro, Evgeny and Shumyatsky, P. (2011) Nilpotency of finite groups with Frobenius groups of automorphisms. Monatshefte fur Mathematik, 163 (4). pp. 461470. ISSN 00269255
Full content URL: http://link.springer.com/article/10.1007%2Fs00605...
Documents 

PDF
__ddat02_staffhome_jpartridge_art%3A10.1007%2Fs0060501001988.pdf  Whole Document Restricted to Repository staff only 161kB 
Item Type:  Article 

Item Status:  Live Archive 
Abstract
Suppose that a finite group G admits a Frobenius group of automorphisms BC of coprime order with kernel B and complement C such that C G (C) is abelian. It is proved that if B is abelian of rank at least two and [C G (u),C G (v),…,C G (v)]=1 for any u,v∈B∖{1} , where C G (v) is repeated k times, then G is nilpotent of class bounded in terms of k and C only. It is also proved that if B is abelian of rank at least three and C G (b) is nilpotent of class at most c for every b∈B∖{1} , then G is nilpotent of class bounded in terms of c and C. The proofs are based on results on graded Lie rings with many commuting components.
Keywords:  Frobenius group, Centralizer, Nilpotent, Graded Lie ring, Primary 20D45, Secondary 17B70, 20D15, 20F40 

Subjects:  G Mathematical and Computer Sciences > G100 Mathematics 
Divisions:  College of Science > School of Mathematics and Physics 
Related URLs:  
ID Code:  15585 
Deposited On:  12 Nov 2014 15:58 
Repository Staff Only: item control page