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

Authors

  • Subrata Majumdar Department of Mathematics University of Rajshahi, Rajshahi
  • Nasima Akter Department of Mathematics University of Rajshahi, Rajshahi

Keywords:

Group presentation, Metacyclic group, Heisenberg group, Free resolution, Huebschmann perturbation method, Homology, Cohomology

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/ganit.v31i0.10304

GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 31 (2011) 9-22

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Published

2012-04-09

How to Cite

Computation of Homology and cohomology groups of a metacyclic group and a factor group of the Heisenberg Group. (2012). GANIT: Journal of Bangladesh Mathematical Society, 31, 9-22. https://doi.org/10.3329/ganit.v31i0.10304

Issue

Vol. 31 (2011)

Section

Articles

License

The copyright of GANIT: Journal of Bangladesh Mathematical Society is reserved by Bangladesh Mathematical Society (web: https://bdmathsociety.org/)

How to Cite

Computation of Homology and cohomology groups of a metacyclic group and a factor group of the Heisenberg Group. (2012). GANIT: Journal of Bangladesh Mathematical Society, 31, 9-22. https://doi.org/10.3329/ganit.v31i0.10304