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20.52 (2022)

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A famous result of Burnside states that if $k(G)$ is the number of conjugacy classes of a finite group $G$ of odd order, then $|G| - k(G)$ is divisible by 16. Is it true that for every integer $m > 0$ there exists a finite non-abelian group $G(m)$ of odd order such that $|G(m)| - k(G(m)) = 16m$?

Contributor: D. MacHale

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