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

• Autorzy: Olga Dashkova
• Języki publikacji: 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.

Słowa kluczowe

EN

RG-module; A soluble group; A noetherian R-module

Kategorie tematyczne

• 20H25: Other matrix groups over rings
• 20F16: Solvable groups, supersolvable groups

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 4
• Strony: 922-928

Daty

wydano

2011-08-01

online

2011-05-26

Twórcy

autor

Olga Dashkova

• University of Dnepropetrovsk

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

Identyfikatory

DOI

10.2478/s11533-011-0033-z