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arXiv · 2610.33615

Counterexamples to congruences in finite p-groups

Benjamin Sambale
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Abstract

Let $K$ be a conjugacy class of a finite $p$-group $G$. Héthelyi, Külshammer and the author asked whether the number of conjugacy classes contained in $KK^{-1}$ is always congruent to $1$ modulo $p-1$, and whether, dually, the number of irreducible constituents of $χ\overlineχ$ is congruent to $1$ modulo $p-1$ for every $χ\in\mathrm{Irr}(G)$. We construct a group of order $7^7$ for which both congruences fail.

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Benjamin Sambale. 2026-10-24. Counterexamples to congruences in finite p-groups. https://arxiv.org/abs/2610.33615

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