On Cayley graphs of virtually free groups

Abstract

In 1985, Dunwoody showed that finitely presentable groups are accessible. Dunwoody's result was used to show that context-free groups, groups quasi-isometric to trees or finitely presentable groups of asymptotic dimension 1 are virtually free. Using another theorem of Dunwoody of 1979, we study when a group is virtually free in terms of its Cayley graph and we obtain new proofs of the mentioned results and other previously depending on them.

Cited by in corpus (5)

• Context-Free Groups and Their Structure Trees
• The domino problem on groups of polynomial growth
• Geometric characterizations of virtually free groups
• Generalizations of the Muller-Schupp theorem and tree-like inverse graphs
• The structure of quasi-transitive graphs avoiding a minor with applications to the domino problem