Groups, Geometry, and Dynamics

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Volume 6, Issue 1, 2012, pp. 155–220
DOI: 10.4171/GGD/154

Published online: 2012-02-08

The fully residually $F$ quotients of $F *\langle x,y \rangle$

Nicholas W. M. Touikan[1]

(1) Parc Scientifique et Technologique de Luminy, Marseille, France

We describe the fully residually $F$ groups, or limit groups relative to $F$, that are quotients of $F *\langle x,y \rangle$. We use the structure theory of finitely generated fully residually free groups to produce a finite list of possible types of cyclic JSJ decompositions modulo $F$ that can arise. We also give bounds on uniform hierarchical depth.

Keywords: Limit groups, equations over free groups

Touikan Nicholas W. M.: The fully residually $F$ quotients of $F *\langle x,y \rangle$. Groups Geom. Dyn. 6 (2012), 155-220. doi: 10.4171/GGD/154