On totally inert simple groups

• Autorzy: Martyn Dixon , Martin Evans , Antonio Tortora
• 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

EN

Inert; Totally inert; Simple group

Kategorie tematyczne

• 20F24: FC-groups and their generalizations
• 20E32: Simple groups

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2010
• Tom: 8
• Numer: 1
• Strony: 22-25

Daty

wydano

2010-02-01

online

2010-02-02

Twórcy

autor

Martyn Dixon

• University of Alabama

autor

Martin Evans

• University of Alabama

autor

Antonio Tortora

• Università di Salerno

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

Identyfikatory

DOI

10.2478/s11533-009-0067-7