On Rationality of Verbal Subsets In a Group

Details On Rationality of Verbal Subsets In a Group On Rationality of Verbal Subsets In a Group

2011-03-24

arxiv.org/abs/1103.4817v2

Mathematics

Group Theory

14 pages

Scientific paper

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.

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