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2011 | 9 | 4 | 922-928
Tytuł artykułu

Modules over group rings of soluble groups with a certain condition of maximality

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EN
Abstrakty
EN
Let A be an R G-module, where R is an integral domain and G is a soluble group. Suppose that C G(A) = 1 and A/C A(G) is not a noetherian R-module. Let L nnd(G) be the family of all subgroups H of G such that A/C A(H) is not a noetherian R-module. In this paper we study the structure of those G for which L nnd(G) satisfies the maximal condition.
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Rocznik
Tom
9
Numer
4
Strony
922-928
Opis fizyczny
Daty
wydano
2011-08-01
online
2011-05-26
Twórcy
Bibliografia
  • [1] Dashkova O.Yu., On a class of modules over group rings of solvable groups with restrictions on some systems of subgroups, Fundam. Prikl. Mat., 2008, 14(7), 111–119 (in Russian)
  • [2] Dashkova O.Yu., Modules over integer group rings of locally soluble groups with restrictions on some systems of subgroups, Dopov. Nats. Akad. Nauk Ukr. Mat. Prirodozn. Tekh. Nauki, 2009, 2, 14–19 (in Russian)
  • [3] Dashkova O.Yu., On a class of modules over group rings of locally soluble groups, Trudy Inst. Mat. i Mekh. Ural. Otd. Ros. Akad. Nauk, 2009, 15(2), 94–98 (in Russian)
  • [4] Dixon M.R., Evans M.J., Kurdachenko L.A., Linear groups with the minimal condition on subgroups of infinite central dimension, J. Algebra, 2004, 277(1), 172–186 http://dx.doi.org/10.1016/j.jalgebra.2004.02.029
  • [5] Dixon M.R., Kurdachenko L.A., Linear groups with infinite central dimension, In: Groups, St. Andrews, 2005, 1, London Math. Soc. Lecture Note Ser., 399, Cambridge University Press, Cambridge, 2007, 306–312
  • [6] Fuchs L., Infinite Abelian Groups, Vol. 1, Mir, Moscow, 1974 (in Russian)
  • [7] Kurdachenko L.A., Groups with minimax classes of conjugate elements, In: Infinite Groups and Related Algebraic Structures, Akad. Nauk Ukrainy, Inst. Mat., Kiev, 1993, 160–177 (in Russian)
  • [8] Kurdachenko L.A., Subbotin I.Ya., Linear groups with the maximal condition on subgroups of infinite central dimension, Publ. Mat., 2006, 50(1), 103–131
  • [9] Muñoz-Escolano J.M., Otal J., Semko N.N., The structure of infinite dimensional linear groups satisfying certain finiteness conditions, Algebra Discrete Math., 2009, 8(4), 120–134
  • [10] Wehrfritz B.A.F., Infinite Linear Groups, Ergeb. Math. Grenzgeb., 76, Springer, New York-Heidelberg, 1973
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-011-0033-z
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