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A topological proof in group theory

Published online by Cambridge University Press:  24 October 2008

D. E. Cohen
D. E. Cohen
Affiliation:
University of Birmingham
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Extract

The topological theory of covering spaces may be used to prove results in group theory, for instance, the Kuros-Reidemeister-Schreier theorem (1). It seems likely that such methods can be applied to prove the Freiheitsatz (4) and the identity theorem (3), and also perhaps Lyndon's conjecture, that the normal closure in a free group F of a, single element r is freely generated by conjugates of r. However, although these problems may easily be stated in topological terms, no such proof is at present known. In this paper we prove a related result.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 59 , Issue 2 , April 1963 , pp. 277 - 282
Copyright
Copyright © Cambridge Philosophical Society 1963

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References

REFERENCES

(1)Baer, R., and Levi, F., Freie Produkte und ihrer Untergruppen. Compositio Math. 3 (1930), 391–398.Google Scholar
(2)Hilton, P. J., and Wylie, S., Homology theory (Cambridge, 1960).CrossRefGoogle Scholar
(3)Lyndon, R. C., Dependence and independence in free groups. J. Reine Angew. Math. 210 (1962), 148–174.CrossRefGoogle Scholar
(4)Magnus, W., Uber diskontinuierliche Gruppen mit einer definierenden Relation. J. Reine Angew. Math. 163 (1930), 141–165.CrossRefGoogle Scholar
(5)Neumann, H., Generalised free products with amalgamated subgroups. II. American J. Math. 71 (1949), 491–540.CrossRefGoogle Scholar