Hostname: page-component-cb9f654ff-kl2l2 Total loading time: 0 Render date: 2025-08-14T12:20:11.678Z Has data issue: false hasContentIssue false
  • English
  • Français

An identity theorem for multi-relator groups

Published online by Cambridge University Press:  24 October 2008

William A. Bogley
William A. Bogley
Affiliation:
Tufts University, Medford MA 02155, U.S.A. Dartmouth College, Hanover NH 03755, U.S.A.
Rights & Permissions [Opens in a new window]

Extract

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.

In this paper, the Identity Theorem of R. C. Lyndon and the Freiheitssatz of W. Magnus are extended to a large class of multi-relator groups. Included are the two-relator groups introduced by I. L. Anshel in her thesis, where the Freiheitssatz was proved for those groups. The Identity Theorem provides cohomology computations and a classification of finite subgroups. The methods are geometric; technical tools include the original theorems of Magnus and Lyndon, as well as an amalgamation technique due to J. H. C. Whitehead.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 109 , Issue 2 , March 1991 , pp. 313 - 321
Copyright
Copyright © Cambridge Philosophical Society 1991

References

REFERENCES

[1]Anshel, I. L.. A Freiheitssatz for a class of two-relator groups. Ph.D. Thesis, Columbia University (1989).Google Scholar
[2]Chiswell, I., Collins, D. and Huebschmann, J.. Aspherical group presentations. Math. Z. 178 (1981), 1–36.CrossRefGoogle Scholar
[3]Dyer, E. and Vasquez, A. T.. Some small aspherical spaces. J. Austral. Math. Soc. 16 (1973), 332–352.CrossRefGoogle Scholar
[4]Howie, J. and Schneebeli, H. R.. Groups of finite quasi-projective dimension. Comment. Math. Helv. 54 (1979), 615–628.CrossRefGoogle Scholar
[5]Huebschmann, J.. Cohomology theory of aspherical groups and of small cancellation groups. J. Pure Appl. Algebra 14 (1979), 137–143.CrossRefGoogle Scholar
[6]Lyndon, R. C.. Cohomology theory of groups with a single defining relation. Ann. of Math. 52 (1950), 650–665.CrossRefGoogle Scholar
[7]Magnus, W.. Über diskontinuierliche Gruppen mit einer definierenden Relation. (Der Freiheitssatz). J. Reine Angew. Math. 163 (1930), 141–165.CrossRefGoogle Scholar
[8]Whitehead, J. H. C.. On the asphericity of regions in a 3-sphere. Fund. Math. 32 (1939), 149–166.CrossRefGoogle Scholar