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Preprint Number 185

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185. Jakub Gismatullin
Boundedly simple groups of automorphisms of trees
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Submission date: 15 May 2009.

Abstract:

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 colored trees, Tits proved simplicity of automorphism groups generated by stabilizers of edges. We determine for which colored trees such groups are boundedly simple. Namely, for (almost) bi-regular trees they are 32-boundedly simple. For all other colored trees in the class, such groups are not boundedly simple.

Mathematics Subject Classification: Primary 20E08, 20E32; Secondary 05C05, 20E45

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