Commuting elements in conjugacy classes: An application of Hall's Marriage Theorem

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dc.creatorBritnell, John R.
dc.creatorWildon, Mark
dc.date2007-08-28
dc.date2008-10-25
dc.date.accessioned2026-07-07T10:12:45Z
dc.date.available2026-07-07T10:12:45Z
dc.descriptionLet G be a finite group. Define a relation ~ on the conjugacy classes of G by setting C ~ D if there are representatives c \in C and d \in 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 interesting 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.
dc.description11 pages, revised and extended version
dc.identifierhttps://arxiv.org/abs/0708.3872
dc.identifierhttp://arxiv.org/abs/0708.3872
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/172291
dc.subjectGroup Theory
dc.subjectCombinatorics
dc.subject20E45, 05D15; 20D60
dc.titleCommuting elements in conjugacy classes: An application of Hall's Marriage Theorem
dc.typetext

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