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2010 | 8 | 1 | 22-25
Tytuł artykułu

On totally inert simple groups

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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
Wydawca
Czasopismo
Rocznik
Tom
8
Numer
1
Strony
22-25
Opis fizyczny
Daty
wydano
2010-02-01
online
2010-02-02
Twórcy
autor
autor
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
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