| Title:
|
The small Ree group $^{2}G_{2}(3^{2n+1})$ and related graph (English) |
| Author:
|
Asboei, Alireza K. |
| Author:
|
Amiri, Seyed S. S. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
59 |
| Issue:
|
3 |
| Year:
|
2018 |
| Pages:
|
271-276 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $G$ be a finite group. The main supergraph $\mathcal{S}(G)$ is a graph with vertex set $G$ in which two vertices $x$ and $y$ are adjacent if and only if $o(x) \mid o(y)$ or $o(y)\mid o(x)$. In this paper, we will show that $G\cong ^{2}G_{2}(3^{2n+1})$ if and only if $\mathcal{S}(G)\cong \mathcal{S}(^{2}G_{2}(3^{2n+1}))$. As a main consequence of our result we conclude that Thompson's problem is true for the small Ree group $^{2}G_{2}(3^{2n+1})$. (English) |
| Keyword:
|
main supergraph |
| Keyword:
|
simple Ree group |
| Keyword:
|
Thompson's problem |
| MSC:
|
05C25 |
| MSC:
|
20D08 |
| idZBL:
|
Zbl 06940869 |
| idMR:
|
MR3861551 |
| DOI:
|
10.14712/1213-7243.2015.255 |
| . |
| Date available:
|
2018-09-10T12:06:11Z |
| Last updated:
|
2020-10-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147395 |
| . |
| Reference:
|
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| Reference:
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