On recognition of alternating groups by prime graph
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 994-1010
Voir la notice de l'article provenant de la source Math-Net.Ru
The prime graph $GK(G)$ of a finite group $G$ is the graph
whose vertex set is the set of prime divisors of $|G|$ and in which
two distinct vertices $r$ and $s$ are adjacent if and only if there exists an element of $G$ of order $rs$.
Let $Alt_n$ denote the alternating group of degree $n$. Assume that $p\geq13$ is a prime and
$n$ is an integer such that $p\leq n\leq p+3$. We prove that if $G$ is a finite group such that $GK(G)=GK(Alt_n)$,
then $G$ has a unique nonabelian composition factor, and this factor is isomorphic to $Alt_t$, where $p\leq t\leq p+3$.
Keywords:
alternating group, prime graph, simple groups.
@article{SEMR_2017_14_a28,
author = {A. M. Staroletov},
title = {On recognition of alternating groups by prime graph},
journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
pages = {994--1010},
publisher = {mathdoc},
volume = {14},
year = {2017},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SEMR_2017_14_a28/}
}
A. M. Staroletov. On recognition of alternating groups by prime graph. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 994-1010. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a28/