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Free resolutions for certain classes of groups

Published online by Cambridge University Press:  20 January 2009

Subrata Majumdar
Subrata Majumdar
Affiliation:
Rajshahi University, Bangladesh
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In a previous paper [1] we constructed a free resolution for a class of groups which include Fuchsian groups with compact orbit spaces [2, 3], infinite polyhedral groups, plane crystallographic groups p2, p3, p4 and p6 and Dyck's groups [4], and used this resolution for computation of the integral homology and cohomology of these groups. Lyndon [5] determined the cohomology of groups with a single defining relation. The plane crystallographic groups p1 and pg and Artin's braid group B3 are among these groups. In this paper we have constructed free resolutions for certain classes of groups–resolutions which are particularly suitable for direct computation of the homology and the cohomology of these groups for any coefficient module. These classes of groups include the plane crystallographic groups pm, cm and pgg. We have computed the integral homology and cohomology from each of the free resolutions obtained.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 26 , Issue 2 , June 1983 , pp. 173 - 179
Copyright
Copyright © Edinburgh Mathematical Society 1983

References

REFERENCES

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