Simple groups with infinite verbal width and the same positive theory as free groups
Montserrat Casals‐Ruiz, Albert Garreta, Ilya Kazachkov, Javier de la Nuez González · arXiv (Cornell University) · 2019
In this paper we show that there exists an uncountable family of finitely generated simple groups with the same positive theory as any non-abelian free group. In particular, these simple groups have infinite $w$-verbal width for all non-trivial words $w$.