Geodesic
Critical groups of hereditary local superradical formation
Problemy fiziki, matematiki i tehniki, no. 2 (2013), pp. 66-75 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper all critical groups with an identity Frattini subgroup for hereditary local superradical formation are described. New examples of hereditary local superradical formations are obtained.
Mots-clés : formation, simple non-abelian group.
Keywords: superradical formation, critical group 
@article{PFMT_2013_2_a9,
     author = {S. F. Kamornikov and V. N. Tyutyanov},
     title = {Critical groups of hereditary local superradical formation},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {66--75},
     year = {2013},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2013_2_a9/}
}
TY  - JOUR
AU  - S. F. Kamornikov
AU  - V. N. Tyutyanov
TI  - Critical groups of hereditary local superradical formation
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2013
SP  - 66
EP  - 75
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/PFMT_2013_2_a9/
LA  - ru
ID  - PFMT_2013_2_a9
ER  - 
%0 Journal Article
%A S. F. Kamornikov
%A V. N. Tyutyanov
%T Critical groups of hereditary local superradical formation
%J Problemy fiziki, matematiki i tehniki
%D 2013
%P 66-75
%N 2
%U http://geodesic.mathdoc.fr/item/PFMT_2013_2_a9/
%G ru
%F PFMT_2013_2_a9
S. F. Kamornikov; V. N. Tyutyanov. Critical groups of hereditary local superradical formation. Problemy fiziki, matematiki i tehniki, no. 2 (2013), pp. 66-75. http://geodesic.mathdoc.fr/item/PFMT_2013_2_a9/

[1] Nereshennye voprosy teorii grupp: Kourovskaya tetrad, Institut matematiki SO RAN, Novosibirsk, 2006, 194 pp.

[2] V. N. Semenchuk, “Razreshimye $\mathfrak{F}$-radikalnye formatsii”, Matematicheskie zametki, 59:2 (1996), 261–266 | DOI | MR | Zbl

[3] V. N. Semenchuk, L. A. Shemetkov, “Sverkhradikalnye formatsii”, Dokl. NAN Belarusi, 44:5 (2000), 24–26 | MR

[4] V. N. Semenchuk, O. A. Mokeeva, “O probleme klassifikatsii sverkhradikalnykh formatsii”, Izv. vuzov. Matematika, 2008, no. 12, 70–75 | MR | Zbl

[5] Shemetkov L. A., Formatsii konechnykh grupp, Nauka, M., 1978, 272 pp. | MR | Zbl

[6] K. Doerk, T. Hawkes, Finite soluble groups, Walter de Gruyter, Berlin–New York, 1992, 891 pp. | MR

[7] S. F. Kamornikov, M. V. Selkin, Podgruppovye funktory i klassy konechnykh grupp, Belaruskaya navuka, Minsk, 2003, 256 pp.

[8] D. Gorenstein, Konechnye prostye gruppy. Vvedenie v ikh klassifikatsiyu, Mir, M., 1985, 352 pp. | MR | Zbl

[9] M. W. Liebeck, C. E. Prager, J. Saxl, The maximal factorizations of the finite simple groups and their automorphism groups, Memoirs of the Amer. Math. Soc., 86, no. 432, 1990, 150 pp. | MR

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

[11] H. H. Mitchell, “Determination of the ordinary and modular ternary linear groups”, Trans. Amer. Math. Soc., 12 (1911), 207–242 | DOI | MR | Zbl

[12] R. W. Hartley, “Determination of the ternary collineation groups whose coefficient lie in $GF(2^n)$”, Ann. Math., 25:2 (1925), 140–158 | DOI | MR

[13] M. Suzuki, “On a class double transitive groups”, Ann. Math., 75:1 (1962), 105–145 | DOI | MR | Zbl

[14] M. W. Liebeck, J. Saxl, “On the orders of maximal subgroups of the finite exceptional groups of Lie type”, Proc. London Math. Soc., 55 (1987), 299–330 | DOI | MR | Zbl

[15] P. Kleidman, “The maximal subgroups of the Chevalley group $G_2(q)$ with $q$ odd, the Ree groups $^2G_2(q)$ and their automorphism groups”, J. Algebra, 117 (1988), 30–71 | DOI | MR | Zbl

[16] S. A. Syskin, “Ob odnom voprose R. Bera”, Sib. mat. zhurnal, 20:3 (1979), 679–681 | MR | Zbl

[17] K. Zsigmondy, “Zur Theorie der Potenzreste”, Monath. Math. Phis., 3 (1892), 265–284 | DOI | MR | Zbl