Thompson's conjecture for the alternating group of degree $2p$ and $2p+1$

Czechoslovak Mathematical Journal

Azam Babai, Ali Mahmoudifar¹ 

关键词: finite group;    conjugacy class size;    simple group;   

DOI  :  10.21136/CMJ.2017.0396-16

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

  For a finite group $G$ denote by $N(G)$ the set of conjugacy class sizes of $G$. In 1980s, J. G. Thompson posed the following conjecture: If $L$ is a finite nonabelian simple group, $G$ is a finite group with trivial center and $N(G) = N(L)$, then $G\cong L$. We prove this conjecture for an infinite class of simple groups. Let $p$ be an odd prime. We show that every finite group $G$ with the property $Z(G)=1$ and $N(G) = N(A_i)$ is necessarily isomorphic to $A_i$, where $i\in\{2p,2p+1\}$.

【 授权许可】

Unknown