Abstract
We introduce the notion of the k-closure of a group of automorphisms of a locally finite tree, and give several examples of the construction. We show that the k-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.
Funding source: Australian Postgraduate Award
Funding source: Australian Research Council
Award Identifier / Grant number: DP0984342
Funding source: Australian Research Council
Award Identifier / Grant number: DP120100996
Funding source: Australian Research Council
Award Identifier / Grant number: FT110100178
Received: 2013-12-15
Revised: 2014-10-1
Published Online: 2014-11-28
Published in Print: 2015-3-1
© 2015 by De Gruyter
