Product representations of group elements
type: Item
instance of: scholarly article
title: Product representations of group elements
zbMATH Open document ID: 0723.20014
DOI: 10.1007/BF01199057
author: A. C. G. Clement
published in: Archiv der Mathematik
publication date: 1991-01-01T00:00:00Z
review text: Dénes and Hermann proved that given a finite group G, exactly the elements of a suitable coset modulo the derived group of G can be represented as a product of \(| G|\) different elements of G. The aim of this paper is to prove that for \(j<| G|\) each element of G can be represented as a product of j different elements of G unless G is an elementary abelian 2-group, \(j=2\) or \(j=| G| -2\) in which case only the non-identity elements of G are representable as a product of j different elements.
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20F05
zbMATH DE Number: 4191986
zbMATH Keywords: products of group elements
zbMATH Keywords: finite group
MaRDI profile type: Publication
cites work: A note on a finite subset of a group closed under multiplication of distinct elements
cites work: Q4005897
cites work: Q5800830
full work available at URL: https://doi.org/10.1007/bf01199057
OpenAlex ID: W1985397949
description: scientific article; zbMATH DE number 4191986