| Title:
|
On the relations between the central factor-module and the derived submodule in modules over group rings (English) |
| Author:
|
Kurdachenko, Leonid A. |
| Author:
|
Subbotin, Igor Ya. |
| Author:
|
Chupordia, Vasyl A. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
56 |
| Issue:
|
4 |
| Year:
|
2015 |
| Pages:
|
433-445 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A modular analogue of the well-known group theoretical result about finiteness of the derived subgroup in a group with a finite factor by its center has been obtained. (English) |
| Keyword:
|
modules |
| Keyword:
|
group rings |
| Keyword:
|
modules over group rings |
| Keyword:
|
generalized soluble groups |
| Keyword:
|
modules of finite rank |
| Keyword:
|
an integral domain |
| Keyword:
|
a scalar ring |
| Keyword:
|
Schur's theorem |
| Keyword:
|
Baer's theorem |
| MSC:
|
20C07 |
| MSC:
|
20F19 |
| idZBL:
|
Zbl 06537718 |
| idMR:
|
MR3434223 |
| DOI:
|
10.14712/1213-7243.2015.136 |
| . |
| Date available:
|
2015-12-17T11:46:16Z |
| Last updated:
|
2018-01-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144753 |
| . |
| Reference:
|
[1] Baer R.: Representations of groups as quotient groups. II. Minimal central chains of a groups.Trans. Amer. Math. Soc. 58 (1945), 348–389. MR 0015107, 10.1090/S0002-9947-1945-0015107-1 |
| Reference:
|
[2] Baer R.: Endlichkeitskriterien fur Kommutatorgruppen.Math. Ann. 124 (1952), 161–177. Zbl 0046.02202, MR 0045720, 10.1007/BF01343558 |
| Reference:
|
[3] Ballester-Bolinches A., Camp-Mora S., Kurdachenko L.A., Otal J.: Extension of a Schur theorem to groups with a central factor with a bounded section rank.J. Algebra 393 (2013), 1–15. Zbl 1294.20045, MR 3090052, 10.1016/j.jalgebra.2013.06.035 |
| Reference:
|
[4] Dixon M.R., Kurdachenko L.A., Otal J.: Linear analogues of theorems of Schur, Baer and Hall.Int. J. Group Theory 2 (2013), no. 1, 79–89. Zbl 1306.20055, MR 3033535 |
| Reference:
|
[5] Hall P.: Nilpotent groups.Notes of lectures given at the Canadian Math. Congress, University of Alberta, August 1957, pp. 12–30. Zbl 0211.34201 |
| Reference:
|
[6] Kargapolov M.I., Merzlyakov Yu.I.: Fundamentals of the theory of groups.Nauka, Moscow, 1982. MR 0677282 |
| Reference:
|
[7] Kurdachenko L.A., Otal J.: The rank of the factor-group modulo the hypercenter and the rank of the some hypocenter of a group.Cent. Eur. J. Math. 11 (2013), no. 10, 1732–1741. Zbl 1316.20039, MR 3080231 |
| Reference:
|
[8] Kurdachenko L.A., Otal J., Subbotin I.Ya.: Artinian Modules over Group Rings.Frontiers in Mathematics, Birkhäuser, Basel, 2007, 248 p. Zbl 1110.16001, MR 2270897 |
| Reference:
|
[9] Kurosh A.G.: The Theory of Groups.Nauka, Moscow, 1967. Zbl 0111.02502, MR 0249495 |
| Reference:
|
[10] Lucchini A.: A bound on the number of generators of a finite group.Archiv. Math. (Basel) 53 (2013), 313–31. Zbl 0679.20028, MR 1015993, 10.1007/BF01195209 |
| Reference:
|
[11] Neumann B.H.: Groups with finite classes of conjugate elements.Proc. London Math. Soc. 1 (1951), 178–187. Zbl 0043.02401, MR 0043779 |
| Reference:
|
[12] Robinson D.J.S.: Finiteness Conditions and Generalized Soluble Groups.Part 1. Springer, Berlin, 1972, xv+210 pp. Zbl 0243.20033, MR 0332989 |
| Reference:
|
[13] Saeedi F., Veisi B.: On Schur's theorem and its converses for n-Lie algebras.Linear Multilinear Algebra 62 (2014), no. 9, 1139–1145. Zbl 1307.17007, MR 3250935, 10.1080/03081087.2013.809871 |
| Reference:
|
[14] Schur I.: Über die Darstellungen der endlichen Gruppen durch gebrochene lineare substitutionen.J. reine angew. Math., 127 (1904), 20–50. MR 1580631 |
| Reference:
|
[15] Stewart I.N.: Verbal and marginal properties of non-associative algebras in the spirit of infinite group theory.Proc. London Math. Soc. 28 (1974), 129–140. MR 0338095 |
| Reference:
|
[16] Wehrfritz B.A.F.: Infinite Linear Groups.Springer, Berlin, 1973. Zbl 0261.20038, MR 0335656 |
| Reference:
|
[17] Wiegold J.: Multiplicators and groups with finite central factor-groups.Math. Z. 89 (1965), 345–347. Zbl 0134.03002, MR 0179262, 10.1007/BF01112166 |
| . |
