The mechanical computation of first and second cohomology groups

  • Authors:

  • D. F. Holt

  • Affiliations:

  • Mathematics Institute, University of Warwick, Coventry CV4 7AL, Great Britain

  • Venue:
  • Journal of Symbolic Computation
  • Year:
  • 1985

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Abstract

We describe the theory and implementation of computer algorithms designed to compute the dimensions of the first and second cohomology groups of a finite group G, acting on a finite module M defined over a field K of prime order. Presentations of extensions of M by G can also be computed. The method is to find a Sylow p-subgroup P of G, where p =@?K@?, to compute H^x (P, M) first, using variants of the Nilpotent Quotient Algorithm, and then to compute H^x (G, M) as the subgroup of stable elements of H^x (P, M).