Dimension of elementary amenable groups
The paper has three parts. It is conjectured that for every elementary amenable group G and every non-zero commutative ring k, the homological dimension of G over k is equal to the Hirsch length of G whenever G has no k-torsion. In Part I this is proved for several classes, including the abelian-by-...
| Những tác giả chính: | , |
|---|---|
| Định dạng: | Journal article |
| Được phát hành: |
2012
|
| _version_ | 1826286225052401664 |
|---|---|
| author | Bridson, M Kropholler, P |
| author_facet | Bridson, M Kropholler, P |
| author_sort | Bridson, M |
| collection | OXFORD |
| description | The paper has three parts. It is conjectured that for every elementary amenable group G and every non-zero commutative ring k, the homological dimension of G over k is equal to the Hirsch length of G whenever G has no k-torsion. In Part I this is proved for several classes, including the abelian-by-polycyclic groups. In Part II it is shown that elementary amenable groups of homological dimension one are filtered colimits of systems of groups of cohomological dimension one. Part III is devoted to the deeper study of cohomological dimension with particular emphasis on the nilpotent-by-polycyclic case. |
| first_indexed | 2024-03-07T01:40:36Z |
| format | Journal article |
| id | oxford-uuid:96b8a6fb-aabd-45b3-a122-a6b2d2d5817c |
| institution | University of Oxford |
| last_indexed | 2024-03-07T01:40:36Z |
| publishDate | 2012 |
| record_format | dspace |
| spelling | oxford-uuid:96b8a6fb-aabd-45b3-a122-a6b2d2d5817c2022-03-26T23:54:54ZDimension of elementary amenable groupsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:96b8a6fb-aabd-45b3-a122-a6b2d2d5817cSymplectic Elements at Oxford2012Bridson, MKropholler, PThe paper has three parts. It is conjectured that for every elementary amenable group G and every non-zero commutative ring k, the homological dimension of G over k is equal to the Hirsch length of G whenever G has no k-torsion. In Part I this is proved for several classes, including the abelian-by-polycyclic groups. In Part II it is shown that elementary amenable groups of homological dimension one are filtered colimits of systems of groups of cohomological dimension one. Part III is devoted to the deeper study of cohomological dimension with particular emphasis on the nilpotent-by-polycyclic case. |
| spellingShingle | Bridson, M Kropholler, P Dimension of elementary amenable groups |
| title | Dimension of elementary amenable groups |
| title_full | Dimension of elementary amenable groups |
| title_fullStr | Dimension of elementary amenable groups |
| title_full_unstemmed | Dimension of elementary amenable groups |
| title_short | Dimension of elementary amenable groups |
| title_sort | dimension of elementary amenable groups |
| work_keys_str_mv | AT bridsonm dimensionofelementaryamenablegroups AT krophollerp dimensionofelementaryamenablegroups |