On Rationality of Verbal Subsets In a Group

Abstract

Let $F$ be a free non-abelian group. We show that for any group word $w$ the set $w[F]$ of all values of $w$ in $F$ is rational in $F$ if and only if $w[F]=1$ or $w[F]=F.$ We generalize this to a wide class of free products of groups.

14 pages

Cited by in corpus (2)

• Verbal subgroups of hyperbolic groups have infinite width
• Solution sets for equations over free groups are EDT0L languages -- ICALP 2015 version