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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
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Category: math
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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
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Date available: 2018-09-10T12:06:11Z
Last updated: 2020-10-05
Stable URL: http://hdl.handle.net/10338.dmlcz/147395
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