Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
A subgroup H of a group G is inert if |H: H ∩ H g| is finite for all g ∈ G and a group G is totally inert if every subgroup H of G is inert. We investigate the structure of minimal normal subgroups of totally inert groups and show that infinite locally graded simple groups cannot be totally inert.
Słowa kluczowe
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
22-25
Opis fizyczny
Daty
wydano
2010-02-01
online
2010-02-02
Twórcy
autor
- University of Alabama, mdixon@as.ua.edu
autor
- University of Alabama, mevans@as.ua.edu
autor
- Università di Salerno, antortora@unisa.it
Bibliografia
- [1] Belyaev V.V., Inert subgroups in infinite simple groups, Sibirsk. Mat. Zh., 1939, 34(4), 17–23 (in Russian), English translation: Siberian Math. J., 1993, 34(4), 606–611
- [2] Belyaev V.V., Locally finite groups containing a finite inseparable subgroup, Sibirsk. Mat. Zh., 1993, 34, 23–41 (in Russian), English translation: Siberian Math. J., 1993, 34, 218–232
- [3] Belyaev V.V., Inert subgroups in simple locally finite groups, In: Finite and locally finite groups, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 471, 213–218, Kluwer Acad. Publ., Dordrecht, 1995
- [4] Belyaev V.V., Kuzucuoǧlu M., Seçkin E., Totally inert groups, Rend. Sem. Mat. Univ. Padova, 1999, 102, 151–156
- [5] Bergman G. M., Lenstra H. W. Jr., Subgroups close to normal subgroups, J. Algebra, 1989, 127(1), 80–97 http://dx.doi.org/10.1016/0021-8693(89)90275-5
- [6] Dixon M.R., Evans M. J., Smith H., Embedding groups in locally (soluble-by-finite) simple groups, J. Group Theory, 2006, 9, 383–395 http://dx.doi.org/10.1515/JGT.2006.026
- [7] Kegel O.H., Wehrfritz B.A.F., Locally finite groups, North Holland, Amsterdam, 1973
- [8] Neumann H., Varieties of groups, Springer-Verlag, NewYork, 1967
- [9] Olshanskii A.Yu., An infinite group with subgroups of prime orders, Izv. Akad. Nauk SSSR Ser. Mat., 1980, 44(2), 309–321
- [10] Robinson D.J.S., Finiteness conditions and generalized soluble groups, Springer-Verlag, 1972
- [11] Robinson D.J.S., A course in the theory of groups, 2nd edition, Springer-Verlag, NewYork, 1996
- [12] Robinson D.J.S., On inert subgroups of a group, Rend. Sem. Mat. Univ. Padova, 2006, 115, 137–159
- [13] Zel’manov E.I., Solution of the restricted Burnside’s problem for groups of odd exponent, Math. USSR-Izv., 1991, 36(1), 41–60 http://dx.doi.org/10.1070/IM1991v036n01ABEH001946
- [14] Zel’manov E.I., Solution of the restricted Burnside problem for 2-groups, Mat. Sb., 1991, 182(4), 568–592 (in Russian), English translation: Math. USSR-Sb., 1992, 72(2), 543–565
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-009-0067-7