Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-29T18:58:15.359Z Has data issue: false hasContentIssue false
  • English
  • Français

Projective resolutions for graph products

Published online by Cambridge University Press:  20 January 2009

Daniel E. Cohen
Daniel E. Cohen
Affiliation:
School of Mathematical SciencesQueen Mary and Westfield CollegeMile End RoadLondon E1 4NSEnglandE-mail address: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let Γ be a finite graph together with a group Gv at each vertex v. The graph productG(Γ) is obtained from the free product of all Gv by factoring out by the normal subgroup generated by for all adjacent v, w.

In this note we construct a projective resolution for G(Γ) given projective resolutions for each Gv, and obtain some applications.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 38 , Issue 1 , February 1995 , pp. 185 - 188
Copyright
Copyright © Edinburgh Mathematical Society 1995

References

REFERENCES

1.Baik, Y.-G., Howie, J. and Pride, S. J., The identity problem for graph products, J. Algebra 162 (1993), 168–177.CrossRefGoogle Scholar
2.Bass, H., Euler characteristics and characters of discrete groups, Invent. Math. 35 (1976), 155–196.CrossRefGoogle Scholar
3.Brown, K. S., Cohomology of groups (Graduate texts in mathematics 87, Springer-Verlag, 1982).CrossRefGoogle Scholar
4.Chiswell, I. M., Euler characteristics of groups, Math. Z. 147 (1976), 1–11.CrossRefGoogle Scholar
5.Chiswell, I. M., The Euler characteristic of graph products and Coxeter groups, Discrete groups and geometry (Harvey, W. J. and MacLachlan, C., eds., London Mathematical Society Lecture Notes 173, Cambridge University Press, 1992), 36–46.Google Scholar
6.Green, E. R., Graph products of groups (Ph.D. Thesis, University of Leeds, 1990).Google Scholar
7.Hattori, A., Rank elements of a projective module, Nagoya Math. J. 25 (1965), 113–120.CrossRefGoogle Scholar
8.Stallings, J. R., Centerless groups—an algebrain formulation of Gottlieb's theorem, Topology 4 (1965), 129–134.CrossRefGoogle Scholar
9.Swan, R. G., Groups of cohomological dimension one, J. Alg. 12 (1969), 585–610.CrossRefGoogle Scholar