Abelian generalized Frobenius complements for p-groups and the Hughes problem
type: Item
instance of: scholarly article
title: Abelian generalized Frobenius complements for p-groups and the Hughes problem
zbMATH Open document ID: 0617.20005
DOI: 10.1007/BF01190223
published in: Archiv der Mathematik
publication date: 1988-01-01T00:00:00Z
review text: Let G be a finite group, M a complex module for G, N the normal subgroup of G generated by the elements of G that have a nontrivial centralizer in M. The factor group G/N is called a generalized Frobenius complement for G. The structure of G/N is studied in this paper. The main result is: If G is a finite p-group of odd order, and G is either abelian-by-cyclic or of maximal class, then all the generalized Frobenius complements for G are abelian. Applications to the Hughes problem are given.
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 20D40
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 4000195
zbMATH Keywords: finite p-group
zbMATH Keywords: generalized Frobenius complements
zbMATH Keywords: Hughes problem
author: Carlo Maria Scoppola
MaRDI profile type: Publication
cites work: A nonabelian Frobenius–Wielandt complement
cites work: On the Hughes problem for exponent \(p^ 2\)
cites work: Endliche Gruppen I
cites work: Generalized Frobenius Complements
cites work: Verallgemeinerte Hughes-Untergruppen endlicher Gruppen
cites work: Q3743477
description: scientific article; zbMATH DE number 4000195