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

Open Mathematics (2011)

- Volume: 9, Issue: 4, page 922-928
- ISSN: 2391-5455

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topOlga Dashkova. "Modules over group rings of soluble groups with a certain condition of maximality." Open Mathematics 9.4 (2011): 922-928. <http://eudml.org/doc/269638>.

@article{OlgaDashkova2011,

abstract = {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.},

author = {Olga Dashkova},

journal = {Open Mathematics},

keywords = {RG-module; A soluble group; A noetherian R-module; modules over group rings; soluble groups; Noetherian modules},

language = {eng},

number = {4},

pages = {922-928},

title = {Modules over group rings of soluble groups with a certain condition of maximality},

url = {http://eudml.org/doc/269638},

volume = {9},

year = {2011},

}

TY - JOUR

AU - Olga Dashkova

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

JO - Open Mathematics

PY - 2011

VL - 9

IS - 4

SP - 922

EP - 928

AB - 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.

LA - eng

KW - RG-module; A soluble group; A noetherian R-module; modules over group rings; soluble groups; Noetherian modules

UR - http://eudml.org/doc/269638

ER -

## References

top- [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) Zbl1170.20301
- [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 Zbl1055.20042
- [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 Zbl1125.20040
- [6] Fuchs L., Infinite Abelian Groups, Vol. 1, Mir, Moscow, 1974 (in Russian) Zbl0274.20067
- [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) Zbl0900.20062
- [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 Zbl1132.20029
- [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 Zbl1199.20082
- [10] Wehrfritz B.A.F., Infinite Linear Groups, Ergeb. Math. Grenzgeb., 76, Springer, New York-Heidelberg, 1973

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