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TitleComputing group resolutions
Author(s) Graham Ellis
TypeArticle in Journal
AbstractWe 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.
KeywordsEilenberg–Mac Lane space, Finite group, Automatic group, Free resolution, Cohomology, GAP implementation
URL http://www.sciencedirect.com/science/article/pii/S0747717104000343
JournalJournal of Symbolic Computation
Pages1077 - 1118
Translation No
Refereed No