Action of a Frobenius-like group with kernel having central derived subgroup

Download

index.pdf

Date

2016-09-01

Author

Ercan, Gülin

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

364
views

172
downloads

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 [F, h] = F for all nonidentity elements h is an element of H. Suppose that a finite group G admits a Frobenius-like group of auto-morphisms FH of coprime order with [F', H] = 1. In case where C-G( F) = 1 we prove that the groups G and C-G( H) have the same nilpotent length under certain additional assumptions.

Subject Keywords

Frobenius-like group, Fixed Points, Nilpotent Length

URI

https://hdl.handle.net/11511/48783

Journal

INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION

DOI

https://doi.org/10.1142/s0218196716500533

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

On the influence of fixed point free nilpotent automorphism groups Ercan, Gülin (2017-12-01) 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 for all nonidentity elements . Let FH be a Frobenius-like group with complement H of prime order such that is of prime order. Suppose that FH acts on a finite group G by automorphisms where in such a way that In the present paper we prove that the Fitting series of coincides with the intersections of with the Fitting series of G, and the nilpotent length of G exceeds the...
Action of a Frobenius-like group Güloǧlu, Ismail Ş.; Ercan, Gülin (2014-03-15) We call a finite group Frobenius-like if it has a nontrivial nilpotent normal subgroup F possessing a nontrivial complement H such that [F, h] = F for all nonidentity elements h is an element of H. We prove that any irreducible nontrivial FH-module for a Frobenius-like group FH of odd order over an algebraically closed field has an H-regular direct summand if either F is fixed point free on V or F acts nontrivially on V and the characteristic of the field is coprime to the order of F. Some consequences of t...
Action of a Frobenius-like group with fixed-point free kernel Ercan, Gülin (Walter de Gruyter GmbH, 2014-09-01) We call a finite group Frobenius-like if it has a nontrivial nilpotent normal subgroup F possessing a nontrivial complement H such that [F,h] = F for all nonidentity elements h is an element of H. We prove that any irreducible nontrivial FH-module for a Frobenius-like group FH of odd order over an algebraically-closed field has an H-regular direct summand if either F is fixed-point free on V or F acts nontrivially on V and the characteristic of the field is coprime to the order of F. Some consequences of th...
NILPOTENT LENGTH OF A FINITE SOLVABLE GROUP WITH A FROBENIUS GROUP OF AUTOMORPHISMS Ercan, Gülin; Ogut, Elif (2014-01-01) We prove that a finite solvable group G admitting a Frobenius group FH of automorphisms of coprime order with kernel F and complement H such that [G, F] = G and C-CG(F) (h) = 1 for all nonidentity elements h is an element of H, is of nilpotent length equal to the nilpotent length of the subgroup of fixed points of H.
Frobenius-like groups as groups of automorphisms Ercan, Gülin; Khukhro, Evgeny (2014-01-01) 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 rela...

Citation Formats

G. Ercan, “Action of a Frobenius-like group with kernel having central derived subgroup,” INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, pp. 1257–1265, 2016, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/48783.