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.
Fine, B., Kreuzer, M., & Rosenberger, G. (2015). On Magnus' Freiheitssatz and free polynomial algebras. International Journal of Group Theory, 4(1), 13-19. doi: 10.22108/ijgt.2015.7279
MLA
Benjamin Fine; Martin Kreuzer; Gerhard Rosenberger. "On Magnus' Freiheitssatz and free polynomial algebras". International Journal of Group Theory, 4, 1, 2015, 13-19. doi: 10.22108/ijgt.2015.7279
HARVARD
Fine, B., Kreuzer, M., Rosenberger, G. (2015). 'On Magnus' Freiheitssatz and free polynomial algebras', International Journal of Group Theory, 4(1), pp. 13-19. doi: 10.22108/ijgt.2015.7279
VANCOUVER
Fine, B., Kreuzer, M., Rosenberger, G. On Magnus' Freiheitssatz and free polynomial algebras. International Journal of Group Theory, 2015; 4(1): 13-19. doi: 10.22108/ijgt.2015.7279