The small Ree group 2 G 2 ( 3 2 n + 1 ) and related graph

Alireza K. Asboei; Seyed S. S. Amiri

Commentationes Mathematicae Universitatis Carolinae (2018)

  • Volume: 59, Issue: 3, page 271-276
  • ISSN: 0010-2628

Abstract

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Let G be a finite group. The main supergraph 𝒮 ( G ) is a graph with vertex set G in which two vertices x and y are adjacent if and only if o ( x ) ∣ o ( y ) or o ( y ) ∣ o ( x ) . In this paper, we will show that G ≅ 2 G 2 ( 3 2 n + 1 ) if and only if 𝒮 ( G ) ≅ 𝒮 ( 2 G 2 ( 3 2 n + 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 2 n + 1 ) .

How to cite

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Asboei, Alireza K., and Amiri, Seyed S. S.. "The small Ree group $^{2}G_{2}(3^{2n+1})$ and related graph." Commentationes Mathematicae Universitatis Carolinae 59.3 (2018): 271-276. <http://eudml.org/doc/294221>.

@article{Asboei2018,
abstract = {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 $^\{2\}G_\{2\}(3^\{2n+1\})$.},
author = {Asboei, Alireza K., Amiri, Seyed S. S.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {main supergraph; simple Ree group; Thompson's problem},
language = {eng},
number = {3},
pages = {271-276},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {The small Ree group $^\{2\}G_\{2\}(3^\{2n+1\})$ and related graph},
url = {http://eudml.org/doc/294221},
volume = {59},
year = {2018},
}

TY - JOUR
AU - Asboei, Alireza K.
AU - Amiri, Seyed S. S.
TI - The small Ree group $^{2}G_{2}(3^{2n+1})$ and related graph
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2018
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 59
IS - 3
SP - 271
EP - 276
AB - 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 $^{2}G_{2}(3^{2n+1})$.
LA - eng
KW - main supergraph; simple Ree group; Thompson's problem
UR - http://eudml.org/doc/294221
ER -

References

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