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arXiv · 2206.09547

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

Ilya Gorshkov
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Abstract

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

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Ilya Gorshkov. 2023-02-02. Structure of finite groups with restrictions on the set of conjugacy classes sizes. https://doi.org/10.46298/cm.9722

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