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Frobenius-like groups as groups of automorphisms
Date
2014-01-01
Author
Ercan, Gülin
Güloğlu, İsmail Şuayip
Khukhro, Evgeny
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This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
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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
Journal
TURKISH JOURNAL OF MATHEMATICS
DOI
https://doi.org/10.3906/mat-1403-62
Collections
Department of Mathematics, Article