Details:
Title  Computing group resolutions  Author(s)  Graham Ellis  Type  Article in Journal  Abstract  We describe an algorithm for constructing a reasonably small CWstructure 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 lowdimensional 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  Eilenberg–Mac Lane space, Finite group, Automatic group, Free resolution, Cohomology, GAP implementation  ISSN  07477171 
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 
