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2011 | 9 | 6 | 1344-1348
Tytuł artykułu

Groups whose proper subgroups are Baer-by-Chernikov or Baer-by-(finite rank)

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Our main result is that a locally graded group whose proper subgroups are Baer-by-Chernikov is itself Baer-by-Chernikov. We prove also that a locally (soluble-by-finite) group whose proper subgroups are Baer-by-(finite rank) is itself Baer-by-(finite rank) if either it is locally of finite rank but not locally finite or it has no infinite simple images.
Wydawca
Czasopismo
Rocznik
Tom
9
Numer
6
Strony
1344-1348
Opis fizyczny
Daty
wydano
2011-12-01
online
2011-09-23
Twórcy
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] Chernikov N.S., Theorem on groups of finite special rank, Ukrainian Math. J., 1990, 42(7), 855–861 http://dx.doi.org/10.1007/BF01062091
  • [3] Dixon M.R., Evans M.J., Smith H., Groups with all proper subgroups nilpotent-by-finite rank, Arch. Math. (Basel), 2000, 75(2), 81–91
  • [4] Dixon M.R., Evans M.J., Smith H., Groups with all proper subgroups soluble-by-finite rank, J. Algebra, 2005, 289(1), 135–147 http://dx.doi.org/10.1016/j.jalgebra.2005.01.047
  • [5] Dixon M.R., Evans M.J., Smith H., Embedding groups in locally (soluble-by-finite) simple groups, J. Group Theory, 2006, 9(3), 383–395 http://dx.doi.org/10.1515/JGT.2006.026
  • [6] Franciosi S., de Giovanni F., Sysak Y.P., Groups with many polycyclic-by-nilpotent subgroups, Ricerche Mat., 1999, 48(2), 361–378
  • [7] Kleidman P.B., Wilson R.A., A characterization of some locally finite simple groups of Lie type, Arch. Math. (Basel), 1987, 48(1), 10–14
  • [8] Napolitani F., Pegoraro E., On groups with nilpotent by Černikov proper subgroups, Arch. Math. (Basel), 1997, 69(2), 89–94
  • [9] Newman M.F., Wiegold J., Groups with many nilpotent subgroups, Arch. Math. (Basel), 1964, 15, 241–250
  • [10] Robinson D.J.S., Finiteness Conditions and Generalized Soluble Groups. I, Ergeb. Math. Grenzgeb., 62, Springer, Berlin-Heidelberg-New York, 1972
  • [11] Smith H., More countably recognizable classes of groups, J. Pure Appl. Algebra, 2009, 213(7), 1320–1324 http://dx.doi.org/10.1016/j.jpaa.2008.11.030
  • [12] Wehrfritz B.A.F., Infinite Linear Groups, Ergeb. Math. Grenzgeb., 76, Springer, Berlin-Heidelberg-New York, 1973
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-011-0077-0
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