Geodesic
Finite groups whose maximal subgroups have only soluble proper subgroups
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 1, pp. 237-240.

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We give a description of a finite group whose maximal subgroups possess only soluble proper subgroups, which implies the answer to the well-known question on composition factors of finite groups, whose second maximal subgroups are soluble.
Keywords: finite group, maximal subgroup, solubility. 
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D. V. Lytkina; A. Kh. Zhurtov. Finite groups whose maximal subgroups have only soluble proper subgroups. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 1, pp. 237-240. http://geodesic.mathdoc.fr/item/SEMR_2022_19_1_a8/

[1] J.G. Thompson, “Nonsolvable finite groups all of whose local subgroups are solvable”, Bull. AMS, 74 (1968), 383–437 | DOI | MR | Zbl

[2] J.H. Conway, R.T. Curtis, S.P. Norton, R.A. Parker, R.A. Wilson, Atlas of finite groups. Maximal subgroups and ordinary characters for simple groups. With comput. assist. from J. G. Thackray, Clarendon Press, Oxford, 1985 | MR | Zbl

[3] B. Huppert, Endliche Gruppen, v. I, Springer Verlag, Berlin etc, 1979 | MR | Zbl

[4] V.D. Mazurov, “Minimal permutation representation of finite simple classical groups. Special linear, symplectic, and unitary groups”, Algebra Logic, 32:3 (1993), 142–153 | DOI | MR | Zbl

[5] J.N. Bray, D.F. Holt, C.M. Roney-Dougal, The maximal subgroups of the low-dimensional finite classical groups, London Mathematical Society Lecture Note Series, 407, Cambridge University Press, Cambridge, 2013 | MR | Zbl

[6] A.V. Vasil'ev, V.D. Mazurov, “Minimal permutation representations of finite simple orthogonal groups”, Algebra Logic, 33:6 (1994), 337–350 | DOI | MR | Zbl

[7] A.V. Vasil'ev, “Minimal permutation representations of finite simple exceptional groups of types $G_2$ and $F_4$”, Algebra Logic, 35:6 (1996), 371–383 | DOI | MR | Zbl

[8] A.V. Vasil'ev, “Minimal permutation representations of finite simple exceptional groups of types $E_6$, $E_7$, and $E_8$”, Algebra Logic, 36:5 (1997), 302–310 | DOI | MR | Zbl

[9] A.V. Vasil'ev, “Minimal permutation representations of finite simple exceptional twisted groups”, Algebra Logic, 37:1 (1998), 9–20 | DOI | MR | Zbl