Fraïssé limits of limit groups

Abstract

We modify the notion of a Fraïssé class and show that various interesting classes of groups, notably the class of nonabelian limit groups and the class of finitely generated elementary free groups, admit Fraïssé limits. Furthermore, we rediscover Lyndon's $\mathbb{Z}[t]$-exponential completions of countable torsion-free CSA groups, as Fraïssé limits with respect to extensions of centralizers. Dedicated to the memory of Charles Sims.

Revised version, accepted to J. Algebra