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Ein neuer Beweis eines Satzes von Magnus

Published online by Cambridge University Press:  24 October 2008

U. Stammbach
Affiliation:
Eidgen. Technische Hochschule, Zürich, Switzerland

Summary

The author provides a new and very simple proof of the following theorem of Magnus (2):

Theorem. Let the group G have both a presentation with n + r generators and r relations also a presentation with n generators. Then G is the free group on n generators.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

LITERATUR

(1)Magnus, W.Beziehungen zwischen Gruppen und Idealen in einem speziellen Ring. Math. Ann. 111 (1935), 259280.CrossRefGoogle Scholar
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(3)Stallings, J.Homology and central series of groups. J. Algebra 2 (1965), 170181.CrossRefGoogle Scholar
(4)Stammbach, U.Anwendungen der Homologietheorie der Gruppen auf Zentralreihen und auf Invarianten von Präsentierungen. Math. Z. 94 (1966), 157177.CrossRefGoogle Scholar