Geodesic
Finite simple groups with two maximal subgroups of coprime orders
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 1150-1159

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In 1962, V. A. Belonogov proved that if a finite group $G$ contains two maximal subgroups of coprime orders, then either $G$ is one of known solvable groups or $G$ is simple. In this short note based on results by M. Liebeck and J. Saxl on odd order maximal subgroups in finite simple groups we determine possibilities for triples $(G,H,M)$, where $G$ is a finite nonabelian simple group, $H$ and $M$ are maximal subgroups of $G$ with $(|H|,|M|)=1$.
Keywords: finite group, maximal subgroup, subgroups of coprime orders.
Mots-clés : simple group 
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     author = {N. V. Maslova},
     title = {Finite simple groups with two maximal subgroups of coprime orders},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1150--1159},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a10/}
}
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N. V. Maslova. Finite simple groups with two maximal subgroups of coprime orders. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 1150-1159. http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a10/