| Title | Computing group resolutions |
| Author(s) | Graham Ellis |
| Type | Article in Journal |
| Abstract | We describe an algorithm for constructing a reasonably small CW-structure on the classifying space of a finite or automatic group G. The algorithm inputs a set of generators for G, and its output can be used to compute the integral cohomology of G. A prototype GAP implementation suggests that the algorithm is a practical method for studying the cohomology of finite groups in low dimensions. We also explain how the method can be used to compute the low-dimensional cohomology of finite crossed modules. The paper begins with a review of the notion of syzygy between defining relators for groups. This topological notion is then used in the design of the algorithm. |
| Keywords | |
| ISSN | 0747-7171 |
| URL |
http://www.sciencedirect.com/science/article/pii/S0747717104000343 |
| Language | English |
| Journal | Journal of Symbolic Computation |
| Volume | 38 |
| Number | 3 |
| Pages | 1077 - 1118 |
| Year | 2004 |
| Edition | 0 |
| Translation |
No |
| Refereed |
No |
