## 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 contribution | Commuting conjugacy classes: an application of Hall's marriage theorem to group theory |
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Original language | English |

Pages (from-to) | 795 - 802 |

Number of pages | 8 |

Journal | Journal of Group Theory |

Volume | 12, issue 6 |

DOIs | |

Publication status | Published - Nov 2009 |