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Retracts of vertex sets of trees and the almost stability theorem

Warren Dicks·M. J. Dunwoody
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Abstract

Let G be a group, let T be an (oriented) G-tree with finite edge stabilizers, and let VT denote the vertex set of T. We show that, for each G-retract V' of the G-set VT, there exists a G-tree whose edge stabilizers are finite and whose vertex set is V'. This fact leads to various new consequences of the almost stability theorem. We also give an example of a group G, a G-tree T and a G-retract V' of VT such that no G-tree has vertex set V'.

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BibTeXRIS

Warren Dicks, M. J. Dunwoody. 2006-09-19. Retracts of vertex sets of trees and the almost stability theorem. https://doi.org/10.1515/jgt.2007.051

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