Abstract
The author studies a D G-module A such that D is a Dedekind domain, A/C A (G) is not an Artinian D-module, C A (G) = 1, G is a soluble group, and the system of all subgroups H ≤ G for which the quotient modules A/C A (H) are not Artinian D-modules satisfies the minimum condition. The structure of G is described.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
L. Fuchs, Infinite Abelian Groups. Vol. 2 [Russian translation], Mir, Moscow (1973).
L. A. Kurdachenko, J. Otal, and I. Ya. Subbotin, Artinian Modules over Group Rings, Birkhäuser, Berlin (2007).
L. A. Kurdachenko and I. Ya. Subbotin, Modules over Dedekind Domains, National University, Los Angeles (1996).
L. A. Kurdachenko and I. Ya. Subbotin, “Linear groups with the maximal condition on subgroups of infinite central dimension,” Publ. Mat., 50, 103–131 (2006).
L. A. Kurdachenko, I. Ya. Subbotin, and N. N. Semko, Insight into Modules over Dedekind Domains, National Academy of Sciences of Ukraine, Institute of Mathematics, Kiev (2008).
B. A. F. Wehrfritz, Infinite Linear Groups, Ergebnisse Math. ihrer Grenzgebiete, Springer, Berlin (1973).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 14, No. 7, pp. 111–119, 2008.
Rights and permissions
About this article
Cite this article
Dashkova, O.Y. On a class of modules over group rings of soluble groups with restrictions on some systems of subgroups. J Math Sci 164, 228–233 (2010). https://doi.org/10.1007/s10958-009-9721-7
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-009-9721-7