Group Actions on the Cubic Tree
Marston Conder
DOI: 10.1023/A:1022490600465
Abstract
It is known that every group which acts transitively on the ordered edges of the cubic tree 
3, with finite vertex stabilizer, is isomorphic to one of seven finitely presented subgroups of the full automorphism group of 3-one of which is the modular group. In this paper a complete answer is given for the question (raised by Djokovi 
and Miller) as to whether two such subgroups which intersect in the modular group generate their free product with the modular group amalgamated.
3, with finite vertex stabilizer, is isomorphic to one of seven finitely presented subgroups of the full automorphism group of 3-one of which is the modular group. In this paper a complete answer is given for the question (raised by Djokovi and Miller) as to whether two such subgroups which intersect in the modular group generate their free product with the modular group amalgamated.Pages: 209–218
Keywords: group actions; trees
Full Text: PDF
References
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2. D.Z. Djokovic, "Another example of a finitely presented infinite simple group," J. Algebra, 69 (1981), 261-269.
3. D.Z. Djokovic, Correction, retraction, and addendum to "Another example of a finitely presented infinite simple group," J. Algebra 82 (1983), 285-293.
4. D.Z. Djokovic and G.L. Miller, "Regular groups of automorphisms of cubic graphs," J. Combin. Theory Ser. B 29 (1980), 195-230.
5. W.T. Tutte, "A family of cubical graphs," Proc. Cambridge Philos. Soc. 43 (1947), 459-474.
6. W.T. Time, "On the symmetry of cubic graphs," Canad. J. Math. 11 (1959), 621-624.