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2011 | 9 | 2 | 420-432
Tytuł artykułu

Groups whose all subgroups are ascendant or self-normalizing

Treść / Zawartość
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Języki publikacji
EN
Abstrakty
EN
This paper studies groups G whose all subgroups are either ascendant or self-normalizing. We characterize the structure of such G in case they are locally finite. If G is a hyperabelian group and has the property, we show that every subgroup of G is in fact ascendant provided G is locally nilpotent or non-periodic. We also restrict our study replacing ascendant subgroups by permutable subgroups, which of course are ascendant [Stonehewer S.E., Permutable subgroups of infinite groups, Math. Z., 1972, 125(1), 1–16].
Wydawca
Czasopismo
Rocznik
Tom
9
Numer
2
Strony
420-432
Opis fizyczny
Daty
wydano
2011-04-01
online
2011-02-18
Twórcy
autor
Bibliografia
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  • [18] Kurdachenko L.A., Smith H., Groups with all subgroups either subnormal or self-normalizing, J. Pure Appl. Algebra, 2005, 196(2–3), 271–278 http://dx.doi.org/10.1016/j.jpaa.2004.08.005
  • [19] Miller G.A., Moreno H., Non-abelian groups in which every subgroup is abelian, Trans. Amer. Math. Soc., 1903, 4(4), 389–404
  • [20] Möhres W., Auflösbarkeit von Gruppen, deren Untergruppen alle subnormal sind, Arch. Math. (Basel), 1990, 54(3), 232–235
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  • [28] Smith H., Torsion-free groups with all subgroups subnormal, Arch. Math. (Basel), 2001, 76(1), 1–6
  • [29] Smith H., Torsion-free groups with all non-nilpotent subgroups subnormal, In: Topics in Infinite Groups, Quad. Mat., 8, Dept. Math., Seconda Univ. Napoli, Caserta, 2001, 297–308
  • [30] Smith H., Groups with all non-nilpotent subgroups subnormal, In: Topics in Infinite Groups, Quad. Mat., 8, Dept. Math., Seconda Univ. Napoli, Caserta, 2001, 309–326
  • [31] Stonehewer S.E., Permutable subgroups of infinite groups, Math. Z., 1972, 125(1), 1–16 http://dx.doi.org/10.1007/BF01111111
  • [32] Tomkinson M.J., FC-Groups, Pitman Res. Notes Math. Ser., 96, Pitman, Boston-London-Melbourne, 1994
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-011-0007-1
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