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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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/

[1] M. Aschbacher, “On the maximal subgroups of the finite classical groups”, Invent. Math., 76:3 (1984), 469–514 | DOI | MR | Zbl

[2] V.A. Belonogov, “On maximal subgroups. II”, Izv. Vyssh. Uchebn. Zaved. Mat., 5 (1962), 3–11 | MR | Zbl

[3] J.N. Bray, D.F. Holt, C.M. Roney-Dougal, The maximal subgroups of the low-dimensional finite classical groups, London Math. Soc. Lect. Note Ser., 407, Cambridge University Press, Cambridge, 2013 | MR | Zbl

[4] J.H. Conway, et al., Atlas of finite groups, Clarendon Press, Oxford, 1985 | MR | Zbl

[5] F. Gross, “Conjugacy of odd order Hall subgroups”, Bull. Lond. Math. Soc., 19:4 (1987), 311–319 | DOI | MR | Zbl

[6] P.B. Kleidman, M. Liebeck, The subgroup structure of the finite classical groups, Cambridge University Press, Cambridge etc, 1990 | MR | Zbl

[7] M. Liebeck, J. Saxl, “On point stabilizers in primitive permutation groups”, Commun. Algebra, 19:10 (1991), 2777–2786 | DOI | MR | Zbl

[8] R.A. Wilson et. al., Atlas of finite group representations, https://brauer.maths.qmul.ac.uk/Atlas/v3/

[9] R.A. Wilson, “The odd-local subgroups of the Monster”, J. Aust. Math. Soc., Ser. A, 44:1 (1988), 1–16 | DOI | MR | Zbl

[10] R.A. Wilson, “The maximal subgroups of the Baby Monster, I”, J. Algebra, 211 (1999), 1–14 | DOI | MR | Zbl