Commuting conjugacy classes: an application of Hall's marriage theorem to group theory

JR Britnell, M Wildon

Research output: Contribution to journalArticle (Academic Journal)peer-review

4 Citations (Scopus)

Abstract

Let G be a finite group. Define a relation ~ on the conjugacy classes of G by setting C ~ D if there are representatives c C and d D such that cd = dc. In the case where G has a normal subgroup H such that G/H is cyclic, two theorems are proved concerning the distribution, between cosets of H, of pairs of conjugacy classes of G related by ~. One of the proofs involves an application of the famous marriage theorem of Philip Hall. The paper concludes by discussing some aspects of these theorems and of the relation ~ in the particular cases of symmetric and general linear groups, and by mentioning an open question related to Frobenius groups.
Translated title of the contributionCommuting conjugacy classes: an application of Hall's marriage theorem to group theory
Original languageEnglish
Pages (from-to)795 - 802
Number of pages8
JournalJournal of Group Theory
Volume12, issue 6
DOIs
Publication statusPublished - Nov 2009

Bibliographical note

Publisher: de Gruyter

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