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2014 | 12 | 12 | 1762-1771
Tytuł artykułu

On the structure of groups whose non-abelian subgroups are subnormal

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The main aim of this article is to examine infinite groups whose non-abelian subgroups are subnormal. In this sense we obtain here description of such locally finite groups and, as a consequence we show several results related to such groups.
Wydawca
Czasopismo
Rocznik
Tom
12
Numer
12
Strony
1762-1771
Opis fizyczny
Daty
wydano
2014-12-01
online
2014-07-20
Twórcy
Bibliografia
  • [1] Ballester-Bolinches, Kurdachenko L.A., Otal J., Pedraza T., Infinite groups with many permutable subgroups, Rev. Mat. Iberoam., 2008, 24(3), 745–764 http://dx.doi.org/10.4171/RMI/555
  • [2] Berkovich Y., Groups of Prime Power Order, vol. 1, de Gruyter Exp. Math., 46, Berlin, 2008
  • [3] Dixon M.R., Sylow Theory, Formations and Fitting classes in Locally Finite Groups, World Sci. Publ. Co., Singapore, 1994 http://dx.doi.org/10.1142/2386
  • [4] Dixon M.R., Subbotin I.Ya., Groups with finiteness conditions on some subgroup systems: a contemporary stage, Algebra Discrete Math., 2009, 4, 29–54
  • [5] Hall P., Some sufficient conditions for a group to be nilpotent, Illinois J. Math., 1958, 2, 787–801
  • [6] Knyagina V.N., Monakhov V.S., On finite groups with some subnormal Schmidt subgroups, Sib. Math. J., 2004, 45(6), 1316–1322 http://dx.doi.org/10.1023/B:SIMJ.0000048922.59466.20
  • [7] Kurdachenko L.A., Otal J., Subbotin I.Ya., Groups with Prescribed Quotient Groups and Associated Module Theory, World Sci. Publ. Co., New Jersey, 2002
  • [8] Kurdachenko L.A., Otal J., Subbotin I.Ya., Artian Modules over Group Rings, Front. Math., Birkhäuser, Basel, 2007
  • [9] Kurdachenko L.A., Otal J., On the existence of normal complement to the Sylow subgroups of some infinite groups, Carpathian J. Math., 2013, 29(2), 195–200
  • [10] Kuzenny N.F., Semko N.N., The structure of soluble non-nilpotent metahamiltonian groups, Math. Notes, 1983, 34(2), 179–188
  • [11] Kuzenny N.F., Semko N.N., The structure of soluble metahamiltonian groups, Dokl. Akad. Nauk Ukrain. SSR Ser. A, 1985, 2, 6–8
  • [12] Kuzenny N.F., Semko, N.N., On the structure of non-periodic metahamiltonian groups, Russian Math. (Iz. VUZ), 1986, 11, 32–40
  • [13] Kuzenny N.F., Semko N.N., The structure of periodic metabelian metahamiltonian groups with a non-elementary commutator subgroup, Ukrainian Math. J., 1987, 39(2), 180–185
  • [14] Kuzenny N.F., Semko N.N., The structure of periodic metabelian metahamiltonian groups with an elementary commutator subgroup of rank two, Ukrainian Math. J., 1988, 40(6), 627–633 http://dx.doi.org/10.1007/BF01057181
  • [15] Kuzenny N.F., Semko N.N., The structure of periodic non-abelian metahamiltonian groups with an elementary commutator subgroup of rank three, Ukrainian Math. J., 1989, 41(2), 153–158 http://dx.doi.org/10.1007/BF01060379
  • [16] Kuzenny N.F., Semko, N.N., Metahamiltonian groups with elementary commutator subgroup of rank two, Ukrainian Math. J., 1990, 42(2), 149–154 http://dx.doi.org/10.1007/BF01071007
  • [17] Lennox J.C., Stonehewer S.E., Subnormal Subgroups of Groups, Oxford Math. Monogr., Oxford University Press, New York, 1987
  • [18] Mahnev A.A., Finite metahamiltonian groups, Ural. Gos. Univ. Mat. Zap., 1976, 10(1), 60–75
  • [19] Möhres W., Auflösbarkcit von Gruppen deren Untergruppen alle subnormal sind., Arch. Math., 1990, 54(3), 232–235 http://dx.doi.org/10.1007/BF01188516
  • [20] Nagrebetskij V.T., Finite groups every non-nilpotent subgroup of which is normal, Ural. Gos. Univ. Mat. Zap., 1966, 6(3), 45–49
  • [21] Nagrebetskij V.T., Finite nilpotent groups every non-abelian subgroup of which is normal, Ural. Gos. Univ. Mat. Zap., 1967, 6(1), 80–88
  • [22] Robinson D.J.S., Finiteness Conditions and Generalized Soluble Groups, vol. 2, Ergeb. Math. Grenzgeb., 63, Springer, Berlin-Heidelberg-New York, 1972 http://dx.doi.org/10.1007/978-3-662-07241-7
  • [23] Romalis G.M., Sesekin N.F., Metahamiltonian groups I, Ural. Gos. Univ. Mat. Zap., 1966, 5(3), 101–106
  • [24] Romalis G.M., Sesekin N.F., Metahamiltonian groups II, Ural. Gos. Univ. Mat. Zap., 1968, 6(3), 50–52
  • [25] Romalis G.M., Sesekin N.F., The metahamiltonian groups III, Ural. Gos. Univ. Mat. Zap., 1970, 7(3), 195–199
  • [26] Schur I., Über die Darstellungen der endlichen Gruppen durch gebrochene lineare substitutione, J. Reine Angew. Math., 1904, 127, 20–50
  • [27] Smith H., Torsion free groups with all non-nilpotent subgroups subnormal, In: Topics in infinite groups, Quad. Mat., 8, Seconda Università degli Studi di Napoli, Caserta, 2001, 297–308
  • [28] Smith H., Groups with all non-nilpotent subgroup subnormal, In: Topics in infinite groups, Quad. Mat., 8, Seconda Università degli Studi di Napoli, Caserta, 2001, 309–326
  • [29] Stonehewer S.E., Formations and a class of locally soluble groups, Proc. Cambridge Phil. Soc., 1966, 62, 613–635 http://dx.doi.org/10.1017/S0305004100040275
  • [30] Vedernikov V.A., Finite groups with subnormal Schmidt subgroups, Sib. Algebra Logika, 2007, 46(6), 669–687
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-014-0444-8
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