Geodesic
Some results on the main supergraph of~finite~groups
Algebra and discrete mathematics, Tome 30 (2020) no. 2, pp. 172-178

Voir la notice de l'article provenant de la source Math-Net.Ru

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 $G\cong \mathrm{PSL}(2,p)$ or $\mathrm{PGL}(2,p)$ if and only if $\mathcal{S}(G)\cong \mathcal{S}(\mathrm{PSL}(2,p))$ or $\mathcal{S}(\mathrm{PGL}(2,p))$, respectively. Also, we will show that if $M$ is a sporadic simple group, then $G\cong M$ if only if $\mathcal{S}(G)\cong \mathcal{S}(M)$.
Keywords: graph, main supergraph, finite groups, Thompson's problem. 
@article{ADM_2020_30_2_a1,
     author = {A. K. Asboei and S. S. Salehi},
     title = {Some results on the main supergraph of~finite~groups},
     journal = {Algebra and discrete mathematics},
     pages = {172--178},
     publisher = {mathdoc},
     volume = {30},
     number = {2},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2020_30_2_a1/}
}
TY  - JOUR
AU  - A. K. Asboei
AU  - S. S. Salehi
TI  - Some results on the main supergraph of~finite~groups
JO  - Algebra and discrete mathematics
PY  - 2020
SP  - 172
EP  - 178
VL  - 30
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2020_30_2_a1/
LA  - en
ID  - ADM_2020_30_2_a1
ER  - 
%0 Journal Article
%A A. K. Asboei
%A S. S. Salehi
%T Some results on the main supergraph of~finite~groups
%J Algebra and discrete mathematics
%D 2020
%P 172-178
%V 30
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2020_30_2_a1/
%G en
%F ADM_2020_30_2_a1
A. K. Asboei; S. S. Salehi. Some results on the main supergraph of~finite~groups. Algebra and discrete mathematics, Tome 30 (2020) no. 2, pp. 172-178. http://geodesic.mathdoc.fr/item/ADM_2020_30_2_a1/