Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-26T08:41:06.823Z Has data issue: false hasContentIssue false

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

LITERATUR

(1)Magnus, W.Beziehungen zwischen Gruppen und Idealen in einem speziellen Ring. Math. Ann. 111 (1935), 259280.CrossRefGoogle Scholar
(2)Magnus, W.Ueber freie Faktorgruppen und freie Untergruppen gegebener Gruppen. Monatsh. Math. 47 (1939), 307313.CrossRefGoogle Scholar
(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