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2009 | 7 | 2 | 186-199
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Groups with small deviation for non-subnormal subgroups

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We introduce the notion of the non-subnormal deviation of a group G. If the deviation is 0 then G satisfies the minimal condition for nonsubnormal subgroups, while if the deviation is at most 1 then G satisfies the so-called weak minimal condition for such subgroups (though the converse does not hold). Here we present some results on groups G that are either soluble or locally nilpotent and that have deviation at most 1. For example, a torsion-free locally nilpotent with deviation at most 1 is nilpotent, while a Baer group with deviation at most 1 has all of its subgroups subnormal.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
7
Numer
2
Strony
186-199
Opis fizyczny
Daty
wydano
2009-06-01
online
2009-05-24
Twórcy
autor
Bibliografia
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  • [2] Evans M.J., Kim Y., On groups in which every subgroup of infinite rank is subnormal of bounded defect, Comm. Algebra, 2004, 32, 2547–2557 http://dx.doi.org/10.1081/AGB-120037398[Crossref]
  • [3] Franciosi S., de Giovanni F., Groups satisfying the minimal condition on non-subnormal subgroups, In: Infinite Groups 1994, de Gruyter, Berlin, 1995, 63–72
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  • [9] Kurdachenko L.A., Smith H., Groups with the weak minimal condition for non-subnormal subgroups, Ann. Mat. Pura Appl., 1997, 173, 299–312 http://dx.doi.org/10.1007/BF01783473[Crossref]
  • [10] Kurdachenko L.A., Smith H., Groups in which all subgroups of infinite rank are subnormal, Glasg. Math. J., 2004, 46, 83–89 http://dx.doi.org/10.1017/S0017089503001551[Crossref]
  • [11] Kurdachenko L.A., Smith H., Groups with all subgroups either subnormal or self-normalizing, J. Pure Appl. Algebra, 2005, 196, 271–278 http://dx.doi.org/10.1016/j.jpaa.2004.08.005[Crossref]
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  • [14] McConnell J.C., Robson J.C., Noncommutative Noetherian rings, John Wiley & Sons, Ltd., Chichester, 1987
  • [15] Möhres W., Auflösbarkeit von Gruppen, deren Untergruppen alle subnormal sind, Archiv der Math., 1990, 54, 232–235 http://dx.doi.org/10.1007/BF01188516[Crossref]
  • [16] Robinson D.J.S., Finiteness conditions and generalized soluble groups, Springer-Verlag, New York-Berlin, 1972
  • [17] Robinson D.J.S., A new treatment of soluble groups with finiteness conditions on their abelian subgroups, Bull. London Math. Soc., 1976, 8, 113–129 http://dx.doi.org/10.1112/blms/8.2.113[Crossref]
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  • [19] Smith H., Groups with few non-nilpotent subgroups, Glasgow Math. J., 1997, 39, 141–151 http://dx.doi.org/10.1017/S0017089500032031[Crossref]
  • [20] Smith H., Torsion-free groups with all subgroups subnormal, Arch. Math., 2001, 76, 1–6 http://dx.doi.org/10.1007/s000130050533[Crossref]
  • [21] Zaitsev D.I., Locally solvable groups of finite rank, Dokl. Akad. Nauk SSSR, 1978, 240, 257–260
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-009-0012-9
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