Hostname: page-component-6bb9c88b65-2jdt9 Total loading time: 0 Render date: 2025-07-27T22:01:20.352Z Has data issue: false hasContentIssue false
  • English
  • Français

Length functions and pregroups

Published online by Cambridge University Press:  20 January 2009

I. M. Chiswell
I. M. Chiswell
Affiliation:
School of Mathematical Sciences, Queen Mary College, Mile End Road, London El 4NS
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.

The idea of a pregroup was introduced by Stallings and provides an axiomatic setting for a well-known argument, due to van der Waerden, used to prove normal form theorems. Details are provided in [7], Section 3.

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 30 , Issue 1 , February 1987 , pp. 57 - 67
Copyright
Copyright © Edinburgh Mathematical Society 1987

References

REFERENCES

1.Chiswell, I. M., Embedding theorems for groups with an integer-valued length function, Math. Proc. Cambridge Philos. Soc. 85 (1979), 417–429.CrossRefGoogle Scholar
2.Chiswell, I. M., Length functions and free products with amalgamation of groups, Proc. London Math. Soc. 42 (1981), 42–58.CrossRefGoogle Scholar
3.Hurley, B., On length functions and normal forms in groups, Math. Proc. Cambridge Philos. Soc. 84 (1978), 455–464.CrossRefGoogle Scholar
4.Lyndon, R. C., Length functions in groups, Math. Scand. 12 (1963), 209–234.CrossRefGoogle Scholar
5.Nesayef, F. H., Groups generated by elements of length zero and one (Ph.D. thesis, University of Birmingham, 1983).Google Scholar
6.Promislow, D., Equivalence classes of length functions on groups, Proc. London Math. Soc. 51 (1985), 449–477.CrossRefGoogle Scholar
7.Stallings, J. R., Group theory and three-dimensional manifolds (New Haven and London, Yale University Press, 1971).Google Scholar
8.Wall, C. T. C. (ed.), Homological group theory (London Mathematical Society Lecture Note Series 36, Cambridge University Press, 1979).CrossRefGoogle Scholar