Finite simple groups with factorization $G=G_\pi B$, $2\notin\pi$

E. M. Pal'chik

Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 2, pp. 242-249

Résumé

A classification of finite simple groups factorizable by a Hall subgroup of odd order and some proper subgroup is obtained.

Détail

Keywords: finite simple group, factorization, Hall subgroup.

Bibliographie

[1] Gorenstein D., Konechnye prostye gruppy. Vvedenie v ikh klassifikatsiyu, Mir, M., 1982, 352 pp. | MR

[2] Liebeck M. W., Praeger C. E., Saxl J., “The maximal factorizations of the finite simple groups and their automorphism groups”, Memoirs of AMS, 86:432 (1990), 1–151 | DOI | MR

[3] Palchik E. M., “O konechnykh faktorizuemykh gruppakh s khollovym faktorom nechetnogo poryadka”, Vestsi NAN Belarusi, ser. fiz.-mat. n., 2009, no. 4, 30–34 | MR

[4] Arad Z., Fisman E., “On finite factorizable groups”, J. Algebra, 86:2 (1984), 522–548 | DOI | MR | Zbl

[5] Vdovin E. P., Revin D. O., “Khollovy podgruppy nechetnogo poryadka v konechnykh gruppakh”, Algebra i logika, 41:1 (2002), 15–56 | MR | Zbl

[6] Carter R., “Conjugacy classes in the Weil group”, Composito Math., 25:1 (1972), 1–59 | MR | Zbl

[7] 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

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

[9] Ito N., “On the factorizations of the linear fraction of group $LF(2,p^n)$”, Acta Sci. Math. Szeged, 15 (1953), 79–84 | MR | Zbl

[10] Makhnev A. A., “Konechnye gruppy s samotsentralizuyuscheisya podgruppoi poryadka 6”, Algebra i logika, 19:1 (1980), 91–102 | MR | Zbl

[11] Palchik E. M., “O svoistvakh nekotorykh prostykh delitelei poryadkov minizotropnykh torov konechnykh gripp lieva tipa”, Vestsi NAN Belarusi, ser. fiz.-mat. n., 2012, no. 4, 66–71

[12] Wilson R., The Finite simple group, Springer-Verlag, London, 2009, 298 pp. | MR

[13] Vdovin E. P., Revin D. O., “Teoremy silovskogo tipa”, Uspekhi mat. nauk, 66:5(401) (2011), 3–46 | DOI | MR | Zbl

[14] Gross F., “On a conjecture of Philip Hall”, Proc. London Math. Soc., 52:3 (1986), 464–494 | DOI | MR | Zbl

[15] Curtis C. W., Kantor W. M., Seitz G. M., “The 2-trausitive permutation representation of the finite Chevalley groups”, Trans. Amer. Math. Soc., 218 (1976), 1–59 | MR | Zbl

[16] Tyutyanov V. N., Shemetkov L. A., “Troinye faktorizatsii v konechnykh gruppakh”, Dokl. NAN Belarusi, 46:4 (2002), 52–55 | MR | Zbl

[17] Palchik E. M., “O konechnykh faktorizuemykh gruppakh s nilpotentnym khollovym faktorom”, Vestsi NAN Belarusi, ser. fiz.-mat. n., 2009, no. 2, 52–56 | MR

[18] A. A. Kirillov (red.), Seminar po algebraicheskim gruppam, Sb. st., Mir, M., 1973, 315 pp. | MR

[19] Seitz G. M., “The root subgroups for maximal tori in finite groups of Lie type”, Pacific J. Math., 106:1 (1983), 153–244 | DOI | MR | Zbl

[20] Aschbacher M., Kleidman P., “On a conjecture of Quillen and a lemma of Robinson”, Arch. Math., 55:3 (1990), 209–217 | DOI | MR | Zbl

[21] Monakhov V. S., “Konechnye gruppy s khollovymi dobavleniyami k primitivnym podgruppam”, Sib. mat. zhurn., 48:2 (2007), 359–368 | MR | Zbl

[22] Huppert B., Endliche Gruppen, v. I, Springer, Berlin, 1967, 793 pp. | MR | Zbl

[23] Gorenstein D., Lyons R., The local structure of the finite groups of characteristic 2 type, Memoirs AMS, 42, no. 276, 1983, 731 pp. | DOI | MR

[24] Palchik E. M., “Finite simple factorizable groups with a Hall factor”, Tezisy Mezhdunar. konf. po algebre i geometrii, posvyaschen. 80-letiyu so dnya rozhdeniya A. I. Starostina, Izd-vo “UMTs-UPI”, Ekaterinburg, 2011, 189–190

[25] Palchik E. M., “Konechnye prostye faktorizuemye gruppy s khollovym faktorom chetnogo poryadka”, Vestsi NAN Belarusi, ser. fiz.-mat. n., 2013, no. 1, 50–63