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2012 | 10 | 3 | 942-949
Tytuł artykułu

Locally finite groups with all subgroups either subnormal or nilpotent-by-Chernikov

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let G be a locally finite group satisfying the condition given in the title and suppose that G is not nilpotent-by-Chernikov. It is shown that G has a section S that is not nilpotent-by-Chernikov, where S is either a p-group or a semi-direct product of the additive group A of a locally finite field F by a subgroup K of the multiplicative group of F, where K acts by multiplication on A and generates F as a ring. Non-(nilpotent-by-Chernikov) extensions of this latter kind exist and are described in detail.
Wydawca
Czasopismo
Rocznik
Tom
10
Numer
3
Strony
942-949
Opis fizyczny
Daty
wydano
2012-06-01
online
2012-03-24
Twórcy
autor
Bibliografia
  • [1] Asar A.O., Locally nilpotent p-groups whose proper subgroups are hypercentral or nilpotent-by-Chernikov, J. London Math. Soc., 2000, 61(2), 412–422 http://dx.doi.org/10.1112/S0024610799008479
  • [2] Casolo C., On the structure of groups with all subgroups subnormal, J. Group Theory, 2002, 5(3), 293–300
  • [3] Everest G., Ward T., An Introduction to Number Theory, Grad. Texts in Math., 232, Springer, London, 2005
  • [4] Möhres W., Auflösbare Gruppen mit endlichem Exponenten, deren Untergruppen alle subnormal sind. I, II, Rend. Sem. Mat. Univ. Padova, 1989, 81, 255–268, 269–287
  • [5] Napolitani F., Pegoraro E., On groups with nilpotent by Černikov proper subgroups, Arch. Math. (Basel), 1997, 69(2), 89–94 http://dx.doi.org/10.1007/s000130050097
  • [6] Robinson D.J.S., Finiteness Conditions and Generalized Soluble Groups. I, Ergeb. Math. Grenzgeb., 62, Springer, New York-Berlin, 1972
  • [7] Smith H., Hypercentral groups with all subgroups subnormal, Bull. London Math. Soc., 1983, 15(3), 229–234 http://dx.doi.org/10.1112/blms/15.3.229
  • [8] Smith H., Groups with all non-nilpotent subgroups subnormal, In: Topics in Infinite Groups, Quad. Mat., 8, Seconda Università degli Studi di Napoli, Caserta, 2001, 309–326
  • [9] Smith H., On non-nilpotent groups with all subgroups subnormal, Ricerche Mat., 2001, 50(2), 217–221
  • [10] Smith H., Groups with all subgroups subnormal or nilpotent-by-Chernikov, Rend. Sem. Mat. Univ. Padova, 126, 2011, 245–253
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-012-0020-z
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