Relative group cohomology and the Orbit category
| dc.citation.epage | 3243 | en_US |
| dc.citation.issueNumber | 7 | en_US |
| dc.citation.spage | 3220 | en_US |
| dc.citation.volumeNumber | 42 | en_US |
| dc.contributor.author | Pamuk, S. | en_US |
| dc.contributor.author | Yalçın, E. | en_US |
| dc.date.accessioned | 2016-02-08T10:50:01Z | |
| dc.date.available | 2016-02-08T10:50:01Z | |
| dc.date.issued | 2014 | en_US |
| dc.department | Department of Mathematics | en_US |
| dc.description.abstract | Let G be a finite group and ℱ be a family of subgroups of G closed under conjugation and taking subgroups. We consider the question whether there exists a periodic relative ℱ-projective resolution for ℤ when ℱ is the family of all subgroups H ≤ G with rk H ≤ rkG - 1. We answer this question negatively by calculating the relative group cohomology ℱH*(G, F{double-struck}2) where G = ℤ/2 × ℤ/2 and ℱ is the family of cyclic subgroups of G. To do this calculation we first observe that the relative group cohomology ℱH*(G, M) can be calculated using the ext-groups over the orbit category of G restricted to the family ℱ. In second part of the paper, we discuss the construction of a spectral sequence that converges to the cohomology of a group G and whose horizontal line at E 2 page is isomorphic to the relative group cohomology of G. © 2014 Copyright Taylor & Francis Group, LLC. | en_US |
| dc.description.provenance | Made available in DSpace on 2016-02-08T10:50:01Z (GMT). No. of bitstreams: 1 bilkent-research-paper.pdf: 70227 bytes, checksum: 26e812c6f5156f83f0e77b261a471b5a (MD5) Previous issue date: 2014 | en |
| dc.identifier.doi | 10.1080/00927872.2013.776066 | en_US |
| dc.identifier.eissn | 1532-4125 | |
| dc.identifier.issn | 0092-7872 | |
| dc.identifier.uri | http://hdl.handle.net/11693/25758 | |
| dc.language.iso | English | en_US |
| dc.publisher | Taylor & Francis | en_US |
| dc.relation.isversionof | http://dx.doi.org/10.1080/00927872.2013.776066 | en_US |
| dc.source.title | Communications in Algebra | en_US |
| dc.subject | Group cohomology | en_US |
| dc.subject | Higher limits | en_US |
| dc.subject | Orbit category | en_US |
| dc.title | Relative group cohomology and the Orbit category | en_US |
| dc.type | Article | en_US |
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