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2013 | 11 | 12 | 2182-2185
Tytuł artykułu

Groups with every subgroup ascendant-by-finite

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A subgroup H of a group G is called ascendant-by-finite in G if there exists a subgroup K of H such that K is ascendant in G and the index of K in H is finite. It is proved that a locally finite group with every subgroup ascendant-by-finite is locally nilpotent-by-finite. As a consequence, it is shown that the Gruenberg radical has finite index in the whole group.
Wydawca
Czasopismo
Rocznik
Tom
11
Numer
12
Strony
2182-2185
Opis fizyczny
Daty
wydano
2013-12-01
online
2013-10-08
Twórcy
Bibliografia
  • [1] Baer R., Situation der Untergruppen und Struktur der Gruppe, Sitzungsber. Heidelb. Akad. Wiss. Math.-Natur. Kl., 1933, 2, 12–17
  • [2] Buckley J.T., Lennox J.C., Neumann B.H., Smith H., Wiegold J., Groups with all subgroups normal-by-finite, J. Austral. Math. Soc., 1995, 59(3), 384–398 http://dx.doi.org/10.1017/S1446788700037289
  • [3] Dedekind R., Ueber Gruppen, deren sämmtliche Theiler Normaltheiler sind, Math. Ann., 1897, 48(4), 548–561 http://dx.doi.org/10.1007/BF01447922
  • [4] De Falco M., de Giovanni F., Musella C., Group in which every subgroup is permutable-by-finite, Comm. Algebra, 2004, 32(3), 1007–1017 http://dx.doi.org/10.1081/AGB-120027964
  • [5] De Falco M., de Giovanni F., Musella C., Sysak Y.P., The structure of groups whose subgroups are permutable-byfinite, J. Austral. Math. Soc., 2006, 81(1s), 35–47 http://dx.doi.org/10.1017/S1446788700014622
  • [6] Dixon M.R., Sylow Theory, Formations and Fitting Classes in Locally Finite Groups, Ser. Algebra, 2, World Scientific, River Edge, 1994
  • [7] Dixon M.R., Subbotin I.Ya., Groups with finiteness conditions on some subgroup systems: a contemporary stage, Algebra Discrete Math., 2009, 4, 29–54
  • [8] Lennox J.C., Robinson D.J.S., The Theory of Infinite Soluble Groups, Oxford Math. Monogr., Oxford University Press, Oxford, 2004 http://dx.doi.org/10.1093/acprof:oso/9780198507284.001.0001
  • [9] Lennox J.C., Stonehewer S.E., Subnormal Subgroups of Groups, Oxford Math. Monogr., Oxford University Press, New York, 1987
  • [10] Robinson D.J.S., Finiteness Conditions and Generalized Soluble Groups, 1&2, Ergeb. Math. Grenzgeb., 62&63, Springer, Berlin-New York, 1972
  • [11] Schmidt O.Yu., Groups whose all subgroups are special, Mat. Sb., 1924, 31(3–4), 366–372 (in Russian)
  • [12] Stonehewer S.E., Permutable subgroups of infinite groups, Math. Z., 1972, 125(1), 1–16 http://dx.doi.org/10.1007/BF01111111
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-013-0312-y
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