Frobenius-like groups as groups of automorphisms

Date

2014-01-01

Author

Ercan, Gülin
Güloğlu, İsmail Şuayip
Khukhro, Evgeny

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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 C-G(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.

Subject Keywords

Frobenius group, Frobenius-like group, Fixed points, Fitting height, Nilpotency class, Derived length, Rank, Order

URI

https://hdl.handle.net/11511/35047

Collections

Department of Mathematics, Article