Group Actions on the Cubic Tree

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It is known that every group which acts transitively on the ordered edges of the cubic tree Γ3, with finite vertex stabilizer, is isomorphic to one of seven finitely presented subgroups of the full automorphism group of Γ3–one of which is the modular group. In this paper a complete answer is given for the question (raised by Djoković and Miller) as to whether two such subgroups which intersect in the modular group generate their free product with the modular group amalgamated.

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