On $A$-Groups with the Same Index Set as a Nilpotent Group

Wei Zhou, Ilya Gorshkov

Let $G$ be a finite group and $N(G)$ be the set of conjugacy class sizes of $G$. For a prime $p$, let $|G|{|}_p$ be the highest $p$-power dividing some element of $N(G)$. and define…