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On one class of modules over group rings with finiteness restrictions | ||
| International Journal of Group Theory | ||
| مقاله 6، دوره 3، شماره 4، اسفند 2014، صفحه 37-46 اصل مقاله (298.97 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2014.5087 | ||
| نویسنده | ||
| Olga Dashkova* | ||
| Professor of the Branch of Moscow state university in Sevastopol | ||
| چکیده | ||
| The author studies the $\bf R$$G$-module $A$ such that $\bf R$ is an associative ring, a group $G$ has infinite section $p$-rank (or infinite 0-rank), $C_{G}(A)=1$, and for every proper subgroup $H$ of infinite section $p$-rank (or infinite 0-rank respectively) the quotient module $A/C_{A}(H)$ is a finite $\bf R$-module. It is proved that if the group $G$ under consideration is locally soluble then $G$ is a soluble group and $A/C_{A}(G)$ is a finite $\bf R$-module. | ||
| کلیدواژهها | ||
| group ring؛ linear group؛ module | ||
| مراجع | ||
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abelian subgroup rank Illinois J. Math. 16 (4), 533-580
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O. Yu. Dashkova (2010) On one class of modules that are close to Noetherian J. Math. Sci. (N. Y.) 169 (5), 636-643
O. Yu. Dashkova (2012) On modules over integer-valued group rings of locally soluble groups with rank restrictions imposed on subgroups Ukrainian Math. J. 63 (9), 1379-1389
O. Yu. Dashkova (2013) Modules over group rings of solvable groups with rank restrictions on subgroups Siberian Adv. Math. 23 (2), 77-83
O. Yu. Dashkova, M. R. Dixon and L. A. Kurdachenko (2007) Linear groups with rank restrictions on the subgroups of infinite central dimension J. Pure Appl. Algebra 208 (3), 785-795
M. R. Dixon, M. J. Evans and L. A. Kurdachenko (2004) Linear groups with the minimal condition on subgroups of infinite central dimension J. Algebra 277 (1), 172-186
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