Abstract Commensurators of Groups Acting on Rooted Trees |
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Authors: | Claas E Röver |
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Institution: | (1) Department of Mathematics, University of Newcastle-upon-Tyne, Newcastle upon Tyne, NE1 7RU, United Kingdom |
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Abstract: | We show that the abstract commensurator of a nearly level transitive weakly branch group H coincides with the relative commensurator of H in the homeomorphism group of the boundary of the tree on which H acts. It is also shown that the commensurator of an infinite group which is commensurable with its own nth direct power
contains a Higman–Thompson group as a subgroup. Applying these results to the Grigorchuk 2-group G we show that the commensurator of G is a finitely presented infinite simple group. |
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Keywords: | commensurators finitely presented simple groups automorphisms of trees |
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