The primitivity rank of an element w of a free group F is defined as the minimal rank of a subgroup containing w as an imprimitive element. Recent work of Louder and Wilton has shown that there is a strong connection between this quantity and the subgroup structure of the one-relator group F/≪w≫. In particular, they show that one-relator groups whose defining relation has primitivity rank at least 3 cannot contain Baumslag-Solitar subgroups, leading them to conjecture that such groups are hyperbolic. In this talk, I will show how to confirm and strengthen this conjecture, providing some applications.
This video is part of the New York Group Theory Cooperative‘s group theory seminar series.
