Frobenius-like groups as groups of automorphisms

Ercan, Gulin and Guloglu, Ismail Suayip and Khukhro, Evgeny (2014) Frobenius-like groups as groups of automorphisms. Turkish Journal of Mathematics, 38 (6). pp. 965-976. ISSN 1300-0098

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A finite group FH is said to be Frobenius-like if it has a nontrivial nilpotent normal subgroup F with a nontrivial complement H such that FH/[F,F] is a Frobenius group with Frobenius kernel F/[F,F]. Such subgroups and sections are abundant in any nonnilpotent finite group. We discuss several recent results about the properties of a finite group G admitting a Frobenius-like group of automorphisms FH aiming at restrictions on G in terms of CG(H) and focusing mainly on bounds for the Fitting height and related parameters. Earlier such results were obtained for Frobenius groups of automorphisms; new theorems for Frobenius-like groups are based on new representation-theoretic results. Apart from a brief survey, the paper contains the new theorem on almost nilpotency of a finite group admitting a Frobenius-like group of automorphisms with fixed-point-free almost extraspecial kernel

Keywords:Frobenius group, Frobenius-like group, fixed points, Fitting height, nilpotency class, derived length, rank, order, JCOpen
Subjects:G Mathematical and Computer Sciences > G100 Mathematics
Divisions:College of Science > School of Mathematics and Physics
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ID Code:16199
Deposited On:04 Dec 2014 16:15

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