Assume that $ #1{} #1{ {#1}} ≤ = ≤ = ≥ = ≥ = {Pr} {Fr} {Re}m$ and $n$ are two positive integers which do not divide each other. If the set of conjugacy class sizes of primary and biprimary elements of a group $G$ is $\{1, m, n, mn\}$ , we show that up to central factors $G$ is a $\{p,q\}$ -group for two distinct primes $p$ and $q$ .
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Jiang et al. (2014) studied this question.