Structure of finite groups with restrictions on the set of conjugacy
classes sizesArticle
Authors: Ilya Gorshkov
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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 $N(A)=\Omega$, $N(B)=\{1,n\}$, and $n$ is a power of
prime.