Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-10T12:32:00.764Z Has data issue: false hasContentIssue false
  • English
  • Français

A New Proof of a Theoremof Magnus

Published online by Cambridge University Press:  20 November 2018

Sal Liriano
Sal Liriano*
Affiliation:
Department of Mathematics, CUNY Graduate Center, 33 W. 42 Street, New York, NY, USA 10036-8099, e-mail: SAL@groups.sci.ccny.cuny.edu
Rights & Permissions [Opens in a new window]

Abstract

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.

Using naive algebraic geometric methods a new proof of the following celebrated theorem of Magnus is given: Let G be a group with a presentation having n generators and m relations. If G also has a presentation on n − m generators, then G is free of rank n − m.

Keywords

Primary: 20E0520C99Secondary: 14Q99
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 40 , Issue 3 , 01 September 1997 , pp. 352 - 355
Copyright
Copyright © Canadian Mathematical Society 1997

References

[BJ] Birman, Joan, An inverse function theorem for free groups, Proc. Amer. Math. Soc. 41 (1973), 634–638.Google Scholar
[BS] Baumslag, G. and Shalen, P., Affine algebraic sets and some infinite finitely presented groups. In: Essays in Group Theory, Springer Verlag, 1987, 1–14.Google Scholar
[CM] Chandler, B. and Magnus, W., The History of Combinatorial Group Theory: A Case Study in the History of Ideas, Springer-Verlag, New York, 1982.Google Scholar
[CS] Culler, M. and Shalen, P., Varieties of representations and splitting of three manifolds, Ann. of Math. 117 (1983), 109–146.Google Scholar
[S] Stammbach, U., Ein neuer Beweis eines Satzen von Magnus, Proc. Cambridge Philos. Soc. 63 (1967), 929–930.Google Scholar
[M1] Magnus, W., The uses of two by two matrices in combinatorial group theory, a survey, Resultate der Mathematik 4 (1981), 171–192.Google Scholar
[M2] Magnus, W., Uber freie Faktorgruppen und freie Untergruppen Gegebener Gruppen, Monatsch. Math. Phys. 47 (1939), 307–313.Google Scholar
[MD] Mumford, D., Algebraic Geometry 1: Complex Projective Varieties, Grundlehren der mathematischen Wissenschaften 21 (1976).Google Scholar
[SN] Sanov, I. N., A property of representation of a free group, Dokl. Akad. Nauk SSSR 57 (1947), 657–659.Google Scholar