Multiplying a conjugacy class by its inverse in a finite group

2024/02/09 by Beltrán, Antonio, Felipe, María José, Melchor, Carmen · 1 citation
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2402.06274

Abstract

Suppose that G is a finite group and K a non-trivial conjugacy class of G such that KK^-1=1∪ D∪ D^-1 with D a conjugacy class of G. We prove that G is not a non-abelian simple group. We also give arithmetical conditions on the class sizes determining the structure of ⟨ K⟩ and ⟨ D⟩. Furthermore, if D=K is a non-real class, then ⟨ K⟩ is p-elementary abelian for some odd prime p.

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• Orders of commutators and Products of conjugacy classes in finite groups

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