A classification theorem for boundary 2-transitive automorphism groups of trees

Radu, Nicolas
(2017) Inventiones Mathematicae — Vol. 209, n° 1, p. 1-60 (2017)

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  • Radu, NicolasUCLouvain
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Abstract
Let T be a locally finite tree all of whose vertices have valency at least 6. We classify, up to isomorphism, the closed subgroups of Aut(T) acting 2-transitively on the set of ends of T and whose local action at each vertex contains the alternating group. The outcome of the classification for a fixed tree T is a countable family of groups, all containing two remarkable subgroups: a simple subgroup of index <= 8 and (the semiregular analog of) the universal locally alternating group of Burger–Mozes (with possibly infinite index). We also provide an explicit example showing that the statement of this classification fails for trees of smaller degree.
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Radu, N. (2017). A classification theorem for boundary 2-transitive automorphism groups of trees. Inventiones Mathematicae, 209(1), 1-60. https://doi.org/10.1007/s00222-016-0704-2 (Original work published 2017)