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arXiv · 2006.16918

A characterisation of virtually free groups via minor exclusion

A. Khukhro
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Abstract

We give a new characterisation of virtually free groups using graph minors. Namely, we prove that a finitely generated, infinite group is virtually free if and only if for any finite generating set, the corresponding Cayley graph is minor excluded. This answers a question of Ostrovskii and Rosenthal. The proof relies on showing that a finitely generated group that is minor excluded with respect to every finite generating set is accessible, using a graph-theoretic characterisation of accessibility due to Thomassen and Woess.

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A. Khukhro. 2020-06-30. A characterisation of virtually free groups via minor exclusion. https://arxiv.org/abs/2006.16918

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