February 9, 2024Open Access

Multiplying a conjugacy class by its inverse in a finite group

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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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Beltrán et al. (Fri,) studied this question.

synapsesocial.com/papers/68e7b285b6db64358770d424 https://doi.org/https://doi.org/10.48550/arxiv.2402.06274

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