| Title:
|
Thompson's conjecture for the alternating group of degree $2p$ and $2p+1$ (English) |
| Author:
|
Babai, Azam |
| Author:
|
Mahmoudifar, Ali |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
67 |
| Issue:
|
4 |
| Year:
|
2017 |
| Pages:
|
1049-1058 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $i\in \{2p,2p+1\}$. (English) |
| Keyword:
|
finite group |
| Keyword:
|
conjugacy class size |
| Keyword:
|
simple group |
| MSC:
|
20D05 |
| MSC:
|
20D60 |
| idZBL:
|
Zbl 06819572 |
| idMR:
|
MR3736018 |
| DOI:
|
10.21136/CMJ.2017.0396-16 |
| . |
| Date available:
|
2017-11-20T14:56:25Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146966 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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