Simple groups of automorphisms of trees determined by their actions on finite subtrees

Publication Type:
Journal Article
Citation:
Journal of Group Theory, 2015, 18 (2), pp. 235 - 261
Issue Date:
2015-01-01
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© de Gruyter 2015. We introduce the notion of the κ-closure of a group of automorphisms of a locally finite tree, and give several examples of the construction. We show that the κ-closure satisfies a new property of automorphism groups of trees that generalises Tits' Property P. We prove that, apart from some degenerate cases, any non-discrete group acting on a tree with this property contains an abstractly simple subgroup.
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