Boundedly simple groups of automorphisms of trees

Details Boundedly simple groups of automorphisms of trees Boundedly simple groups of automorphisms of trees

2009-05-06

arxiv.org/abs/0905.0913v5

Mathematics

Group Theory

19 pages, 4 figures, 2 tables, revised version (improved presentation)

Scientific paper

A group is boundedly simple if for some constant $N$, every nontrivial conjugacy class generates the whole group in $N$ steps (bounded simplicity implies simplicity). For a large class of trees, Tits proved simplicity of automorphism groups generated by stabilizers of edges. We prove that for only subdivisions of bi-regular trees such groups are boundedly simple (in fact 32-boundedly simple). As a consequence, we show that if a boundedly simple group $G$ acts by automorphisms on a tree and $G$ contains a nontrivial stabilizer of some edge, then there is $G$-invariant subtree which is a subdivision of a bi-regular tree.

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