A new conjecture concerning admissibility of groups
type: Item
instance of: scholarly article
title: A new conjecture concerning admissibility of groups
zbMATH Open document ID: 0687.20026
DOI: 10.1016/S0195-6698(89)80044-7
author: Anthony Donald Keedwell
author: József Dénes
published in: European Journal of Combinatorics
publication date: 1989-01-01T00:00:00Z
review text: A finite group is said to be admissible if it has a permutation mapping \(g\to \theta (g)\) such that the mapping \(g\to g\cdot \theta (g)\) is also a permutation. A necessary condition for a finite group to be admissible is that the product of all its elements in some order is equal to the identity. Another necessary condition is that its Sylow 2-subgroups are not cyclic; both conditions are sufficient for soluble groups. Since the second condition is satisfied for all non-soluble groups, the authors propose as new conjecture: All non-soluble groups are admissible. And the authors prove: Theorem: If G is a non-soluble group there exists an ordering of the elements of G the product of which is the identity element of the group (so, for non-soluble group both necessary conditions are satisfied).
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20D05
zbMATH DE Number: 4125677
zbMATH Keywords: admissible groups
zbMATH Keywords: complete mapping
zbMATH Keywords: permutation mapping
zbMATH Keywords: Sylow 2- subgroups
zbMATH Keywords: non-soluble groups
zbMATH Keywords: ordering of the elements
Wikidata QID: Q123009581
reviewed by: Francisco Pérez-Monasor
MaRDI profile type: Publication
cites work: Q3931622
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full work available at URL: s0195-6698(89)80044-7
OpenAlex ID: W2041669438
description: scientific article; zbMATH DE number 4125677