Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
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.
Słowa kluczowe
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
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