Modules over group rings of groups with restrictions on the system of all proper subgroups
We consider the class M of R{modules where R is an associative ring. Let A be a module over a group ring RG, G be a group and let L(G) be the set of all proper subgroups of G. We suppose that if H 2 L(G) then A=CA(H) belongs to M. We study an RG{module A such that G 6= G0, CG(A) = 1. We consider the...
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| Format: | Article |
| Language: | English |
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University of Isfahan
2015-12-01
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| Series: | International Journal of Group Theory |
| Subjects: | |
| Online Access: | http://www.theoryofgroups.ir/pdf_5504_b2fda9c27d76f5bae4d99c57c8252f39.html |
| Summary: | We consider the class M of R{modules where R is an associative ring. Let A be a module over a group ring RG, G be a group and let L(G) be the set of all proper subgroups of G. We suppose that if H 2 L(G) then A=CA(H) belongs to M. We study an RG{module A such that G 6= G0, CG(A) = 1. We consider the cases: 1) M is the class of all artinian R{modules, R is either the ring of integers or the ring of p{adic integers; 2) M is the class of all nite R{modules, R is an associative ring; 3) M is the class of all nite R{modules, R= F is a nite eld. |
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| ISSN: | 2251-7650 2251-7669 |