On subgroup separability of free-by-cyclic and deficiency 1 groups

Abstract

We show that a free-by-cyclic group with a polynomially growing monodromy is subgroup separable exactly when it is virtually $F_n\times \mathbb{Z}$. We also prove that random deficiency 1 groups are not subgroup separable with positive asymptotic probability.

arXiv comment17 pages, no figures; v2: Section 3 rewritten. Final version, to appear in Bull. Lond. Math. Soc