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Ein neuer Beweis eines Satzes von Magnus

Published online by Cambridge University Press:  24 October 2008

U. Stammbach
U. Stammbach
Affiliation:
Eidgen. Technische Hochschule, Zürich, Switzerland
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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
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 4 , October 1967 , pp. 929 - 930
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), 259–280.CrossRefGoogle Scholar
(2)Magnus, W.Ueber freie Faktorgruppen und freie Untergruppen gegebener Gruppen. Monatsh. Math. 47 (1939), 307–313.CrossRefGoogle Scholar
(3)Stallings, J.Homology and central series of groups. J. Algebra 2 (1965), 170–181.CrossRefGoogle Scholar
(4)Stammbach, U.Anwendungen der Homologietheorie der Gruppen auf Zentralreihen und auf Invarianten von Präsentierungen. Math. Z. 94 (1966), 157–177.CrossRefGoogle Scholar