%0 Journal Article
%T On Magnus' Freiheitssatz and free polynomial algebras
%J International Journal of Group Theory
%I University of Isfahan
%Z 2251-7650
%A Fine, Benjamin
%A Kreuzer, Martin
%A Rosenberger, Gerhard
%D 2015
%\ 03/01/2015
%V 4
%N 1
%P 13-19
%! On Magnus' Freiheitssatz and free polynomial algebras
%K Freiheitssatz
%K one-relator group
%K Magnus representation
%K formal power series rings
%R 10.22108/ijgt.2015.7279
%X 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.
%U https://ijgt.ui.ac.ir/article_7279_fcba62ba3131ea087ff25710ba67aa42.pdf