A note on ampleness in the theory of non abelian free groups

Abstract

Recently Ould Houcine-Tent (see arXiv:1205.0929v2 [math.GR]) proved that the theory of non abelian free groups is $n$-ample for any $n<\omega$. We give a sequence of single elements in $F_{\omega }$ witnessing the above mentioned result. Our proof is not independent from the one given in arXiv:1205.0929v2 [math.GR], as we essentially use some theorems from there. On the other hand our witnessing sequence is much simpler.

9 pages

References in corpus (1)

• Ampleness in the free group

Cited by in corpus (2)

• On groups and fields interpretable in torsion-free hyperbolic groups
• On ampleness and pseudo-Anosov homeomorphisms in the free group