A characterisation of virtually free groups

Robert~H.~Gilman, Susan Hermiller, Derek F.~Holt \and Sarah Rees

Keywords

groups, virtually-free, geodesics, word problem, context-free, locally testable, locally excluding

Status

published in Archiv der Mathematik 89 (2007) 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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