Retracts of vertex sets of trees and the almost stability theorem

Warren Dicks, M. J. Dunwoody

Research output: Contribution to journalArticleResearchpeer-review

1 Citation (Scopus)


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′. © Walter de Gruyter 2007.
Original languageEnglish
Pages (from-to)703-721
JournalJournal of Group Theory
Publication statusPublished - 19 Sep 2007


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