Yong Yang

A Huppert-type $\rho^*$--$\sigma^*$ theorem for sub-class sizes

For a finite group $G$, let $\rho^{*}(G)$ be the set of primes dividing some sub-class size of $G$, and let $\sigma^{*}(G)$ be the maximum number of distinct prime divisors of a sub-class size. Motivated by the conjugacy-class version of Huppert's $\rho$--$\sigma$ problem, we prove that \[ |\rho^{*}(G)|<2\sigma^{*}(G)...