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2013 | 11 | 7 | 1177-1187
Tytuł artykułu

On Hall subgroups of a finite group

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
New criteria of existence and conjugacy of Hall subgroups of finite groups are given.
Wydawca
Czasopismo
Rocznik
Tom
11
Numer
7
Strony
1177-1187
Opis fizyczny
Daty
wydano
2013-07-01
online
2013-04-26
Twórcy
autor
  • Department of Mathematics, University of Science and Technology of China, Jinzhai Str. 96, Hefei, 230026, China, wbguo@ustc.edu.cn
  • Department of Mathematics, Francisk Skorina Gomel State University, Sovetskaya Str. 204, Gomel, 246019, Belarus, alexander.skiba49@gmail.com
Bibliografia
  • [1] Ballester-Bolinches A., Esteban-Romero R., Asaad M., Products of Finite Groups, de Gruyter Exp. Math., 53, Walter de Gruyter, Berlin, 2010 http://dx.doi.org/10.1515/9783110220612[Crossref]
  • [2] Čunihin S.A., On π-separate groups, Doklady Akad. Nauk SSSR (N.S.), 1948, 59, 443–445 (in Russian)
  • [3] Čunihin S.A., On weakening the conditions in theorems of Sylow type, Doklady Akad. Nauk SSSR (N.S.), 1952, 83, 663–665 (in Russian) [WoS]
  • [4] Čunihin S.A., On existence and conjugateness of subgroups of a finite group, Mat. Sb. (N.S.), 1953, 33(75), 111–132 (in Russian)
  • [5] Doerk K., Hawkes T., Finite Soluble Groups, de Gruyter Exp. Math., 4, Walter de Gruyter, Berlin, 1992 http://dx.doi.org/10.1515/9783110870138
  • [6] Foguel N., On seminormal subgroups, J. Algebra, 1994, 165(3), 633–635 http://dx.doi.org/10.1006/jabr.1994.1135[Crossref]
  • [7] Guo W., Shum K.P., Skiba A.N., X-semipermutable subgroups of finite groups, J. Algebra, 2007, 315(1), 31–41 http://dx.doi.org/10.1016/j.jalgebra.2007.06.002[Crossref]
  • [8] Guo W.B., Skiba A.N., Criteria of existence of Hall subgroups in non-soluble finite groups, Acta Math. Sin. (Engl. Ser.), 2010, 26(2), 295–304 http://dx.doi.org/10.1007/s10114-010-8034-6[Crossref][WoS]
  • [9] Guo W., Skiba A.N., New criterions of existence and conjugacy of Hall subgroups of finite groups, Proc. Amer. Math. Soc., 2011, 139(7), 2327–2336 http://dx.doi.org/10.1090/S0002-9939-2010-10675-5[Crossref]
  • [10] Hall P., A characteristic property of soluble groups, J. London Math. Soc., 1937, s1–12(3), 198–200 http://dx.doi.org/10.1112/jlms/s1-12.2.198[Crossref]
  • [11] Hall P., Theorems like Sylow’s, Proc. London Math. Soc., 1956, 6, 286–304 http://dx.doi.org/10.1112/plms/s3-6.2.286[Crossref]
  • [12] Kegel O.H., Produkte nilpotenter Gruppen, Arch. Math. (Basel), 1961, 12, 90–93 http://dx.doi.org/10.1007/BF01650529[Crossref]
  • [13] Kegel O.H, Sylow-Gruppen and Subnormalteiler endlicher Gruppen, Math. Z., 1962, 78, 205–221 http://dx.doi.org/10.1007/BF01195169[Crossref]
  • [14] Knyagina V.N., Monakhov V.S., On the π′-properties of a finite group possessing a Hall π-subgroup, Sib. Math. J., 2011, 52(2), 234–243 http://dx.doi.org/10.1134/S0037446611020066[Crossref]
  • [15] Revin D.O., Vdovin E.P., Hall subgroups of finite groups, In: Ischia Group Theory 2004, Naples, March 31–April 3, 2004 Contemp. Math., 402, American Mathematical Society/Bar-Ilan University, Providence/Ramat Gan, 2006, 229–265
  • [16] Rusakov S.A., Analogues of Sylow’s theorem on the existence and imbedding of subgroups, Sibirsk. Mat. Zh., 1963, 4(2), 325–342 (in Russian)
  • [17] Shemetkov L.A., On Sylow properties of finite groups, Dokl. Akad. Nauk BSSR, 1972, 16(10), 881–883 (in Russian)
  • [18] Shemetkov L.A., Formations of Finite Groups, Nauka, Moscow, 1978 (in Russian)
  • [19] Vdovin E.P., Revin D.O., A conjugacy criterion for Hall subgroups in finite groups, Sib. Math. J., 2010, 51(3), 402–409 http://dx.doi.org/10.1007/s11202-010-0041-4[Crossref]
  • [20] Wielandt H., Zum Satz von Sylow. II, Math. Z., 1959, 71, 461–462 http://dx.doi.org/10.1007/BF01181418[Crossref]
  • [21] Wielandt H., Subnormal Subgroups and Permutation Groups, Ohio State University, Columbus, 1971
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-013-0239-3
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