Geodesic
Nonabelian composition factors of a finite group with arithmetic constraints to nonsolvable maximal subgroups
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 2, pp. 122-134 Cet article a éte moissonné depuis la source Math-Net.Ru

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We obtain a complete description of nonabelian composition factors of a finite group in which any nonsolvable maximal subgroup has a primary index. We also complete V. A. Vedernikov's description of nonabelian composition factors of a finite group in which any nonsolvable maximal subgroup is a Hall subgroup.
Keywords: finite group, maximal subgroup, solvable subgroup, Hall subgroup, composition factor, primary index. 
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E. N. Demina; N. V. Maslova. Nonabelian composition factors of a finite group with arithmetic constraints to nonsolvable maximal subgroups. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 2, pp. 122-134. http://geodesic.mathdoc.fr/item/TIMM_2014_20_2_a10/

[1] Vasilev A. V., “Minimalnye podstanovochnye predstavleniya konechnykh prostykh isklyuchitelnykh grupp skruchennogo tipa”, Algebra i logika, 37:1 (1998), 17–35 | MR

[2] Vedernikov V. A., “Konechnye gruppy, v kotorykh kazhdaya nerazreshimaya maksimalnaya podgruppa khollova”, Tr. In-ta matematiki i mekhaniki UrO RAN, 19, no. 3, 2013, 71–82

[3] Kondratev A. S., Gruppy i algebry Li, Izd-vo IMM UrO RAN, Ekaterinburg, 2009, 310 pp.

[4] Kondratev A. S., “Podgruppy konechnykh grupp Shevalle”, Uspekhi mat. nauk, 41:1 (1986), 57–96 | MR | Zbl

[5] Maslova N. V., “Klassifikatsiya maksimalnykh podgrupp nechetnogo indeksa v konechnykh prostykh klassicheskikh gruppakh”, Tr. In-ta matematiki i mekhaniki UrO RAN, 14, no. 4, 2008, 100–118

[6] Maslova N. V., “Maksimalnye podgruppy nechetnogo indeksa v konechnykh gruppakh s prostym lineinym, unitarnym ili simplekticheskim tsokolem”, Algebra i logika, 50:2 (2011), 189–208 | MR | Zbl

[7] Maslova N. V., “Neabelevy kompozitsionnye faktory konechnoi gruppy, vse maksimalnye podgruppy kotoroi khollovy”, Sib. mat. zhurn., 53:5 (2012), 1065–1076 | MR | Zbl

[8] Maslova N. V., Revin D. O., “Konechnye gruppy, v kotorykh vse maksimalnye podgruppy khollovy”, Mat. tr., 15:2 (2012), 105–126 | MR

[9] Aschbacher M., Finite group theory, Cambridge Univ. Press, Cambridge, 1986, 274 pp. | MR | Zbl

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

[11] Baryshovets P. P., “Finite nonsolvable groups in which subgroups of nonprimary index are nilpotent or are Shmidt groups”, Ukrain. Math. J., 33:1 (1981), 37–39 | DOI | MR | Zbl

[12] Bray J. N., Holt D. F., Roney-Dougal C. M., The maximal subgroups of the low-dimensional finite classical groups, Cambridge Univ. Press, Cambridge, 2013, 438 pp. | MR | Zbl

[13] Carter R. W., Simple groups of Lie Type, John Wiley and Sons, London, 1972, 339 pp. | MR | Zbl

[14] J. H. Conway [et. al.], Atlas of finite groups, Clarendon Press, Oxford, 1985, 252 pp. | MR | Zbl

[15] Giudici M., Maximal subgroups of almost simple groups with socle $PSL(2,q)$, arXiv: math/0703685

[16] Gorenstein D., Finite groups, Chelsea Publishing Company, N.Y., 1968, 519 pp. | MR

[17] Gorenstein D., Lyons R., Solomon R., The classification of the finite simple groups, Number 3, Part I, Math. Surveys Monogr., 40, no. 3, Amer. Math. Soc., Providence, 1998, 420 pp. | MR | Zbl

[18] Gross F., “Hall subgroups of order not divisible by 3”, Rocky Mount. J. Math., 23:2 (1993), 569–591 | DOI | MR | Zbl

[19] Guralnick R. M., “Subgroups of prime power index in a simple group”, J. Algebra, 81:2 (1983), 304–311 | DOI | MR | Zbl

[20] Kantor W. M., “Primitive permutation groups of odd degree, and an application to the finite projective planes”, J. Algebra, 106:1 (1987), 15–45 | DOI | MR | Zbl

[21] Kleidman P., Liebeck M.,, The subgroup structure of the finite classical groups, Cambridge University Press, Cambridge, 1990, 303 pp. | MR | Zbl

[22] Liebeck M. W., Praeger C. E., Saxl J., “A classification of the maximal subgroups of the finite alternating and symmetric groups”, J. Algebra, 111:2 (1987), 365–383 | DOI | MR | Zbl

[23] Liebeck M. W., Saxl J., “The primitive permutation groups of odd degree”, J. London Math. Soc. (2), 31:2 (1985), 250–264 | DOI | MR | Zbl

[24] Thompson J. G., “Nonsolvable finite groups all of whose local subgroups are solvable”, Bull. Amer. Math. Soc., 74:3 (1968), 383–437 | DOI | MR | Zbl

[25] Zsigmondy K., “Zur Theorie der Potenzreste”, Monatsh. Math. Phys., 3:1 (1892), 265–284 | DOI | MR | Zbl