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

Title:

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

Creator:

Babai, Azam and Mahmoudifar, Ali

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:15dbabea-742b-47e2-ae8c-ec032d5776e7
uuid:15dbabea-742b-47e2-ae8c-ec032d5776e7
issn:0011-4642

Subject:

matematika, mathematics, finite group, conjugacy class size, simple group, 13, and 51

Type:

model:article and TEXT

Format:

print, bez média, and svazek

Description:

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 $i\in\{2p,2p+1\}$., Azam Babai, Ali Mahmoudifar., and Obsahuje bibliografii

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

1049-1058

Source:

Czechoslovak Mathematical Journal | 2017 Volume:67 | Number:4

Harvested from:

CDK

Metadata only:

false