Fixed points of Frobenius groups of automorphisms

Makarenko, N. Y. and Khukhro, E. I. and Shumyatsky, P. (2011) Fixed points of Frobenius groups of automorphisms. Doklady Mathematics, 83 (2). pp. 152-154. ISSN 1064-5624

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Item Type:Article
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Abstract

A finite group admits a Frobenius automorphisms group FH with a kernel and complement H such that the fixed-point subgroup of F is trivial. It is further proved that every FH-invariant elementary Abelian section of G is a free module for an appropriate prime p. The exponent of a group is bounded with a metacyclic Frobenius group of automorphisms and it is supposed that a finite Frobenius group FH with cyclic kernel F and complement H acts on a finite group G. Bounds for the nilpotency class of groups and Lie rings admitting a metacyclic Frobenius group of automorphisms with fixed-point free kernel are obtained. It is also found that a locally nilpotent torsion-free group G admits a finite Frobenius group of automorphisms FH with cyclic kernel F and complement H of order q.

Additional Information:Original Russian Text © N.Yu. Makarenko, E.I. Khukhro, P. Shumyatsky, 2011, published in Doklady Akademii Nauk, 2011, Vol. 437, No. 1, pp. 20–23. Presented by Academician Yu.L. Ershov August 2, 2010
Keywords:Algebra
Subjects:G Mathematical and Computer Sciences > G100 Mathematics
Divisions:College of Science > School of Mathematics and Physics
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ID Code:15586
Deposited On:01 Jan 2016 19:43

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