Khukhro, E. I. (2000) pgroups of automorphisms of Abelian pgroups. Algebra and Logic, 39 (3). pp. 207214. ISSN 00025232
Full content URL: http://dx.doi.org/10.1007/BF02681764
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Abstract
We consider the action of a pgroup G on an Abelian pgroup A, with the latter treated as a faithful right â�¤,Gmodule. Our aim is to establish a connection between exponents of the kernels under the induced action of G on elementary pgroup ApA and Î©1 and (A) = x â�� A px = 0; the kernels are denoted by CG;(A/pA) and CG(Î©1(A)). respectively. It is proved that if the exponent of one of the kernels CG,(A/pA) or CG(Î©1(A)) is finite then the other also has a finite exponent bounded in terms of the first; moreover, these kernels are nilpotent. In one case we impose the â�� additional restriction â�© piA= 0. And the wreath product Cpâ�� G of a quasicyclic group and i=1 an arbitrary pgroup G shows that this condition cannot be dropped. The results obtained are used to confirm, for one particular case, the conjecture on the boundedness of a derived length of a finite group with an automorphism of order 2 all of whose fixed points are central. (The solubility of such groups, and also the reduction to the case of 2groups, were established in 1.) Â© 2000 Plenum Publishing Corporation.
Keywords:  Algebra, Logic 

Subjects:  G Mathematical and Computer Sciences > G100 Mathematics 
Divisions:  College of Science > School of Mathematics and Physics 
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ID Code:  15741 
Deposited On:  19 Nov 2014 14:25 
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