A characterisation of virtually free groups
Sarah Rees
Keywords
groups, virtually-free, context-free, regular languages, geodesics
Status
published in Arch. Math. (Basel) 89 (2007), no. 4, 289–295.
Abstract
We prove that a finitely generated group $G$ is virtually free if and only if
there exists a generating set for $G$ and $k > 0$ such that all $k$-locally
geodesic words with respect to that generating set are geodesic.
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