| Title:
|
Recognition of some families of finite simple groups by order and set of orders of vanishing elements (English) |
| Author:
|
Khatami, Maryam |
| Author:
|
Babai, Azam |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
68 |
| Issue:
|
1 |
| Year:
|
2018 |
| Pages:
|
121-130 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $G$ be a finite group. An element $g\in G$ is called a vanishing element if there exists an irreducible complex character $\chi $ of $G$ such that $\chi (g)=0$. Denote by ${\rm Vo}(G)$ the set of orders of vanishing elements of $G$. Ghasemabadi, Iranmanesh, Mavadatpour (2015), in their paper presented the following conjecture: Let $G$ be a finite group and $M$ a finite nonabelian simple group such that ${\rm Vo}(G)={\rm Vo}(M)$ and $|G|=|M|$. Then $G\cong M$. We answer in affirmative this conjecture for $M=Sz(q)$, where $q=2^{2n+1}$ and either $q-1$, $q-\sqrt {2q}+1$ or $q+\sqrt {2q}+1$ is a prime number, and $M=F_4(q)$, where $q=2^n$ and either $q^4+1$ or $q^4-q^2+1$ is a prime number. (English) |
| Keyword:
|
finite simple groups |
| Keyword:
|
vanishing element |
| Keyword:
|
vanishing prime graph |
| MSC:
|
20C15 |
| MSC:
|
20D05 |
| idZBL:
|
Zbl 06861570 |
| idMR:
|
MR3783588 |
| DOI:
|
10.21136/CMJ.2018.0355-16 |
| . |
| Date available:
|
2018-03-19T10:26:32Z |
| Last updated:
|
2020-07-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147124 |
| . |
| Reference:
|
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