Finite simple groups all the maximal subgroups of which have $3'$-index
Problemy fiziki, matematiki i tehniki, no. 3 (2020), pp. 67-72.

Voir la notice de l'article provenant de la source Math-Net.Ru

The finite simple non-abelian groups all the maximal subgroups of which have $3'$-index are studied.
Keywords: finite group, maximal subgroup, $3'$-index
Mots-clés : simple non-abelian group.
@article{PFMT_2020_3_a10,
     author = {S. F. Kamornikov and V. N. Tyutyanov},
     title = {Finite simple groups all the maximal subgroups of which have $3'$-index},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {67--72},
     publisher = {mathdoc},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2020_3_a10/}
}
TY  - JOUR
AU  - S. F. Kamornikov
AU  - V. N. Tyutyanov
TI  - Finite simple groups all the maximal subgroups of which have $3'$-index
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2020
SP  - 67
EP  - 72
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PFMT_2020_3_a10/
LA  - ru
ID  - PFMT_2020_3_a10
ER  - 
%0 Journal Article
%A S. F. Kamornikov
%A V. N. Tyutyanov
%T Finite simple groups all the maximal subgroups of which have $3'$-index
%J Problemy fiziki, matematiki i tehniki
%D 2020
%P 67-72
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PFMT_2020_3_a10/
%G ru
%F PFMT_2020_3_a10
S. F. Kamornikov; V. N. Tyutyanov. Finite simple groups all the maximal subgroups of which have $3'$-index. Problemy fiziki, matematiki i tehniki, no. 3 (2020), pp. 67-72. http://geodesic.mathdoc.fr/item/PFMT_2020_3_a10/

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

[2] L.S. Kazarin, “O gruppakh s faktorizatsiei”, DAN SSSR, 256:1 (1981), 26–29

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

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

[5] N.V. Maslova, “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] N.V. Maslova, “Classification of maximal subgroups of odd index in finite simple classical groups”, Siberian Electron. Math. Reports, 15 (2018), 707–718 | MR | Zbl

[7] N.V. Maslova, “Klassifikatsiya maksimalnykh podgrupp nechetnogo indeksa v konechnykh gruppakh so znakoperemennym tsokolem”, Tr. In-ta matematiki i mekhaniki UrO RAN, 16, no. 3, 2010, 182–184

[8] S.F. Kamornikov, V.N. Tyutyanov, “Konechnye prostye gruppy, vse maksimalnye podgruppy kotorykh imeyut nechetnyi indeks”, Problemy fiziki, matematiki i tekhniki, 2020, no. 2 (43), 71–74 | MR

[9] D. Gorenstein, Konechnye prostye gruppy. Vvedenie v ikh klassifikatsiyu, Mir, M., 1985, 352 pp.

[10] J.H. Conway, R.T. Curtis, S.P. Norton, R.A. Parker, R.A. Wilson, Atlas of finite groups, Clarendon Press, Oxford, 1985, 252 pp. | MR | Zbl

[11] G.M. Seitz, “Flag-transitive subgroups of Chevalley groups”, Ann. Math., 97:1 (1973), 27–56 | DOI | MR | Zbl

[12] V.N. Tyutyanov, L.A. Shemetkov, “Troinye faktorizatsii v konechnykh gruppakh”, Doklady NAN Belarusi, 46:2 (2002), 52–55

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

[14] R.A. Wilson, The finite simple groups, Graduate texts in mathematics, 251, Springer, 2009, 298 pp. | DOI | MR | Zbl

[15] J.N. Bray, D.F. Holt, C.M. Roney-Dougal, The maximal subgroups of the low-dimensional finite classical groups, London Math. Soc. Lecture Note Series, 407, Cambridge University Press, 2013, 454 pp. | MR | Zbl