Groups whose elements have given orders
type: Item
instance of: scholarly article
title: Groups whose elements have given orders
zbMATH Open document ID: 0906.20009
DOI: 10.1007/BF02882636
author: Shi Wujie
published in: Chinese Science Bulletin
publication date: 1998-12-07T00:00:00Z
review text: For a finite group \(G\), let \(\pi_e(G)\) be the set of all orders of elements in \(G\) and \(h(G)=h(\pi_e(G))\) be the number of non-isomorphic groups \(H\) such that \(\pi_e(H)=\pi_e(G)\). The author gives a survey of results, obtained mostly by himself, concerning the question: For which finite groups \(G\) is \(h(G)\) finite, infinite, equal to 1?
reviewed by: V. D. Mazurov
Mathematics Subject Classification ID: 20D05
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 1159088
zbMATH Keywords: element orders
zbMATH Keywords: finite simple groups
MaRDI profile type: Publication
cites work: Groups Whose Elements Have Bounded Orders
cites work: Finite Groups in Which Every Element Has Prime Power Order
cites work: On a class of doubly transitive groups
cites work: Classification of Finite Groups with all Elements of Prime Order
cites work: Corrigendum and Addendum to "Classification of Finite Groups with all Elements of Prime Order"
cites work: Finite groups whose element orders are consecutive integers
cites work: A characteristic property ofA 8
cites work: A characterization of some alternating and symmetric groups
cites work: Q4292041
cites work: The characterization of \(\text{PSL}(2,q)\) by its element orders
cites work: A Characterization of Suzuki's Simple Groups
cites work: A characterization of finite simple groups with abelian Sylow \(2\)-subgroups
cites work: Q3729146
cites work: Q4764249
cites work: Q3033953
cites work: A characterization of some orthogonal groups
cites work: Q5287760
cites work: Q3203209
cites work: Q3322282
cites work: Q3785024
cites work: Q3124816
cites work: A simplicity criterion for finite groups
cites work: The set of orders of elements in a finite group
cites work: Q4351826
full work available at URL: https://doi.org/10.1007/bf02882636
OpenAlex ID: W1991799356
description: scientific article; zbMATH DE number 1159088