## Ilya Gorshkov - Structure of finite groups with restrictions on the set of conjugacy classes sizes

cm:9722 - Communications in Mathematics, February 3, 2023, Volume 32 (2024), Issue 1 - https://doi.org/10.46298/cm.9722
Structure of finite groups with restrictions on the set of conjugacy classes sizes

Authors: 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.

Volume: Volume 32 (2024), Issue 1
Published on: February 3, 2023
Accepted on: January 11, 2023
Submitted on: June 22, 2022
Keywords: Mathematics - Group Theory