On Primitive Words I: A New Algorithm

Details On Primitive Words I: A New Algorithm On Primitive Words I: A New Algorithm

2011-03-21

arxiv.org/abs/1103.4061v2

Mathematics

Group Theory

This paper was unified with "On Primitive Words II: Measure Preservation" (arXiv:1104.3991), under the new title "Primitive Wo

Scientific paper

Let $F_k$ be the free group on $k$ generators, and let $H\le J\le \F_k$ be
subgroups of finite rank. We present a new elementary algorithm to determine
whether $H$ is a free factor of $J$. In particular, this algorithm can
determine whether a given element $w\in F_k$ is primitive, i.e. whether it
belongs to some basis of $F_k$.

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