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Title

On Magnus' Freiheitssatz and free polynomial algebras

Year: 1394
COI: JR_THEGR-4-1_004
Language: EnglishView: 20
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Authors

Benjamin Fine - Fairfield University
Martin Kreuzer - University of Passau
Gerhard Rosenberger - University of Hamburg

Abstract:

The Freiheitssatz of Magnus for one-relator groups is one of the cornerstones of combinatorial group theory. In this short note which is mostly expository we discuss the relationship between the Freiheitssatz and corre-sponding results in free power series rings over fields. These are related to results of Schneerson not readily available in English. This relationship uses a faithful representation of free groups due to Magnus. Using this method in free polynomial algebras provides a proof of the Freiheitssatz for one-relation monoids. We show how the classical Freiheitssatz depends on a condition on certain ideals in power series rings in noncommuting variables over fields. A proof of this result over fields would provide a completely dif erent proof of the classical Freiheitssatz.

Keywords:

Paper COI Code

This Paper COI Code is JR_THEGR-4-1_004. Also You can use the following address to link to this article. This link is permanent and is used as an article registration confirmation in the Civilica reference:

https://civilica.com/doc/1199981/

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If you want to refer to this Paper in your research work, you can simply use the following phrase in the resources section:
Fine, Benjamin and Kreuzer, Martin and Rosenberger, Gerhard,1394,On Magnus' Freiheitssatz and free polynomial algebras,https://civilica.com/doc/1199981

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