On the relations between the central factor-module and the derived submodule in modules over group rings

Leonid A. Kurdachenko; Igor Ya. Subbotin; Vasyl A. Chupordia

Commentationes Mathematicae Universitatis Carolinae (2015)

  • Volume: 56, Issue: 4, page 433-445
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Kurdachenko, Leonid A., Subbotin, Igor Ya., and Chupordia, Vasyl A.. "On the relations between the central factor-module and the derived submodule in modules over group rings." Commentationes Mathematicae Universitatis Carolinae 56.4 (2015): 433-445. <http://eudml.org/doc/276171>.

@article{Kurdachenko2015,
abstract = {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.},
author = {Kurdachenko, Leonid A., Subbotin, Igor Ya., Chupordia, Vasyl A.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {modules; group rings; modules over group rings; generalized soluble groups; modules of finite rank; an integral domain; a scalar ring; Schur's theorem; Baer's theorem},
language = {eng},
number = {4},
pages = {433-445},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On the relations between the central factor-module and the derived submodule in modules over group rings},
url = {http://eudml.org/doc/276171},
volume = {56},
year = {2015},
}

TY - JOUR
AU - Kurdachenko, Leonid A.
AU - Subbotin, Igor Ya.
AU - Chupordia, Vasyl A.
TI - On the relations between the central factor-module and the derived submodule in modules over group rings
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2015
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 56
IS - 4
SP - 433
EP - 445
AB - 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.
LA - eng
KW - modules; group rings; modules over group rings; generalized soluble groups; modules of finite rank; an integral domain; a scalar ring; Schur's theorem; Baer's theorem
UR - http://eudml.org/doc/276171
ER -

References

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  9. Kurosh A.G., The Theory of Groups, Nauka, Moscow, 1967. Zbl0111.02502MR0249495
  10. Lucchini A., 10.1007/BF01195209, Archiv. Math. (Basel) 53 (2013), 313–31. Zbl0679.20028MR1015993DOI10.1007/BF01195209
  11. Neumann B.H., Groups with finite classes of conjugate elements, Proc. London Math. Soc. 1 (1951), 178–187. Zbl0043.02401MR0043779
  12. Robinson D.J.S., Finiteness Conditions and Generalized Soluble Groups, Part 1. Springer, Berlin, 1972, xv+210 pp. Zbl0243.20033MR0332989
  13. Saeedi F., Veisi B., 10.1080/03081087.2013.809871, Linear Multilinear Algebra 62 (2014), no. 9, 1139–1145. Zbl1307.17007MR3250935DOI10.1080/03081087.2013.809871
  14. Schur I., Über die Darstellungen der endlichen Gruppen durch gebrochene lineare substitutionen, J. reine angew. Math., 127 (1904), 20–50. MR1580631
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