Geodesic
On the coincidence of Gr\"unberg--Kegel graphs of a~finite simple group and its proper subgroup
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 1, pp. 156-168

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Let $G$ be a finite group. The spectrum of $G$ is the set $\omega(G)$ of orders of its elements. The subset of prime elements of $\omega(G)$ is denoted by $\pi(G)$. The spectrum $\omega(G)$ of a group $G$ defines its prime graph (or Grünberg–Kegel graph) $\Gamma(G)$ with vertex set $\pi(G)$, in which any two different vertices $r$ and $s$ are adjacent if and only if the number $rs$ belongs to the set $\omega(G)$. We describe all the cases when the prime graphs of a finite simple group and of its proper subgroup coincide.
Keywords: finite group, prime spectrum, prime graph (Grünberg–Kegel graph), maximal subgroup.
Mots-clés : simple group 
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     title = {On the coincidence of {Gr\"unberg--Kegel} graphs of a~finite simple group and its proper subgroup},
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N. V. Maslova. On the coincidence of Gr\"unberg--Kegel graphs of a~finite simple group and its proper subgroup. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 1, pp. 156-168. http://geodesic.mathdoc.fr/item/TIMM_2014_20_1_a15/