Abstract
For several years now, I have occupied myself with a project to compute the mod-p cohomology of finite p-groups using computer algebra. To date, programs have been written to build minimal projective resolutions for modules over finite p-groups and create chain maps between resolutions representing cohomology classes. The cup products can be computed by treating them as compositions of chain maps. With this machinery it is possible to find a set of generators and relations for a cohomology ring H*(G, k) in the case that G is a finite p-group and k is a finite field of characteristic p. There are, of course, practical problems that arise if the group or the field is too big. However even for groups and fields of reasonable size, we encounter the problems of producing an output in a form that is usable for interpretation in theoretical investigations and of verifying that the output gives a complete description of the cohomology ring of the group. The description of the algorithms for the actual computation of the cohomology is given in the literature [9, 10, 11]. In this paper, I will focus on some of the problems which still need work.
Partly supported by grants from NSF and the EPSRC
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Carlson, J.F. (1999). Problems in the Calculation of Group Cohomology. In: Dräxler, P., Ringel, C.M., Michler, G.O. (eds) Computational Methods for Representations of Groups and Algebras. Progress in Mathematics, vol 173. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8716-8_5
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DOI: https://doi.org/10.1007/978-3-0348-8716-8_5
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