Structure of finite groups with restrictions on the set of conjugacy classes sizes

Ilya Gorshkov

Let $N(G)$ be the set of conjugacy classes sizes of $G$. We prove that if $N(G)=\Omega \times \{1,n\}$ for specific set $\Omega$ of integers, then $G\simeq A\times B$ where $N(A)=\Omega$, $N(B)=\{…