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. © 2004 Elsevier Ltd. All rights reserved.
CITATION STYLE
Ellis, G. (2004). Computing group resolutions. Journal of Symbolic Computation, 38(3), 1077–1118. https://doi.org/10.1016/j.jsc.2004.03.003
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