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2013 | 11 | 7 | 1188-1196
Tytuł artykułu

On locally graded barely transitive groups

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We show that a barely transitive group is totally imprimitive if and only if it is locally graded. Moreover, we obtain the description of a barely transitive group G for the case G has a cyclic subgroup 〈x〉 which intersects non-trivially with all subgroups and for the case a point stabilizer H of G has a subgroup H 1 of finite index in H satisfying the identity χ(H 1) = 1, where χ is a multi-linear commutator of weight w.
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
11
Numer
7
Strony
1188-1196
Opis fizyczny
Daty
wydano
2013-07-01
online
2013-04-26
Twórcy
autor
  • Department of Mathematics, Middle East Technical University, Ankara, 06531, Turkey, matmah@metu.edu.tr
Bibliografia
  • [1] Arikan A., On locally graded non-periodic barely transitive groups, Rend. Semin. Mat. Univ. Padova, 2007, 117, 141–146
  • [2] Arikan A., Trabelsi N., On certain characterizations of barely transitive groups, Rend. Semin. Mat. Univ. Padova, 2010, 123, 203–210 [WoS]
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  • [5] Belyaev V.V., Kuzucuoglu M., Locally finite barely transitive groups, Algebra Logic, 2003, 42(3), 147–152 http://dx.doi.org/10.1023/A:1023946008218[Crossref]
  • [6] Betin C., Kuzucuoğlu M., Description of barely transitive groups with soluble point stabilizer, Comm. Algebra, 2009, 37(6), 1901–1907 http://dx.doi.org/10.1080/00927870802210076[WoS][Crossref]
  • [7] Bruno B., Phillips R.E., On minimal conditions related to Miller-Moreno type groups, Rend. Sem. Mat. Univ. Padova, 1983, 69, 153–168
  • [8] Bhattacharjee M., Macpherson D., Möller R.G., Neumann P.M., Notes on Infinite Permutation Groups, Texts Read. Math., 12, Lecture Notes in Math., 1698, Hindustan Book Agency/Springer, New Delhi/Berlin, 1997
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  • [11] Hartley B., Kuzucuoğlu M., Non-simplicity of locally finite barely transitive groups, Proc. Edinburgh Math. Soc., 1997, 40(3), 483–490 http://dx.doi.org/10.1017/S0013091500023968[Crossref]
  • [12] Hughes D.R., Thompson J.G., The H-problem and the structure of H-groups, Pacific J. Math., 1959, 9, 1097–1101 http://dx.doi.org/10.2140/pjm.1959.9.1097[Crossref]
  • [13] Kegel O.H., Wehrfritz B.A.F., Locally Finite Groups, North-Holland Math. Library, 3, North-Holland/Elsevier, Amsterdam-London/New York, 1973
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  • [15] Khukhro E.I., Makarenko N.Yu., Large characteristic subgroups satisfying multilinear commutator identities, J. Lond. Math. Soc., 2007, 75(3), 635–646 http://dx.doi.org/10.1112/jlms/jdm047[Crossref]
  • [16] Kuzucuoğlu M., Barely transitive permutation groups, Arch. Math. (Basel), 1990, 55(6), 521–532 http://dx.doi.org/10.1007/BF01191686[Crossref]
  • [17] Kuzucuoğlu M., On torsion-free barely transitive groups, Turkish J. Math., 2000, 24(3), 273–276
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  • [19] Obraztsov V.N., Simple torsion-free groups in which the intersection of any two non-trivial subgroups is non-trivial, J. Algebra, 1998, 199(1), 337–343 http://dx.doi.org/10.1006/jabr.1997.7185[Crossref]
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  • [21] Ol’shanskii A.Yu., Groups of bounded period with subgroups of prime order, Algebra and Logic, 1982, 21(5), 369–418 http://dx.doi.org/10.1007/BF02027230[Crossref]
  • [22] Ol’shanskii A.Yu., Geometry of Defining Relations in Groups, Math. Appl. (Soviet Ser.), 70, Kluwer, Dordrecht, 1991 http://dx.doi.org/10.1007/978-94-011-3618-1[Crossref]
  • [23] Robinson D.J.S., A Course in the Theory of Groups, 2nd ed., Grad. Texts in Math., 80, Springer, New York, 1996 http://dx.doi.org/10.1007/978-1-4419-8594-1
  • [24] Sozutov A.I., Residually finite groups with nontrivial intersections of pairs of subgroups, Siberian Math. J., 2000, 41(2), 362–365 http://dx.doi.org/10.1007/BF02674606[Crossref]
  • [25] Tomkinson M.J., FC-Groups, Res. Notes in Math., 96, Pitman, Boston, 1984
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-013-0240-x
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