Computation of Homology and cohomology groups of a metacyclic group and a factor group of the Heisenberg Group

Abstract

Free resolutions for a metacyclic group M and a factor group G of the Heisenberg group from their presentations constructed by solving system of linear equations over the integral group ring and determined the homology and cohomology groups. The method is straightforward, and the free resolutions are explicitly expressed in terms of the free generators. The resolutions yield the homology and the cohomology groups immediately.DOI: http://dx.doi.org/10.3329/