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arXiv · 1103.4817

On Rationality of Verbal Subsets In a Group

A. Myasnikov·V. Roman'kov
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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.

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A. Myasnikov, V. Roman'kov. 2011-03-24. On Rationality of Verbal Subsets In a Group. https://doi.org/10.1007/s00224-012-9394-3

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