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GROUPS AND LIE RINGS WITH FROBENIUS GROUPS OF AUTOMORPHISMS
- N. YU. MAKARENKO
Ischia Group Theory 201001 Sep 2011
Preview Abstract
In this survey we discuss recent progress in the study of groups and Lie rings admitting a Frobenius group of automorphisms F H with kernel F and complement H. Our main objective is the case, where a finite group G is acted on by F H in such a way that the fixed-point subgroup of the Frobenius kernel is trivial: C_G(F) = 1. Recent results of Khukhro, Makarenko and Shumyatsky show that in this situation various properties of the group G such as the order, rank, nilpotency, nilpotent length, exponent, nilpotency class are close to the corresponding properties of the fixed-point subgroup of the Frobenius complement, C_G(H). Special emphasis is placed on Lie-theoretic methods used for bounding the nilpotency class and exponent of G.

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