A Note on Twisted Conjugacy and Generalized Baumslag-solitar Groups
نویسنده
چکیده
A generalized Baumslag-Solitar group is the fundamental group of a graph of groups all of whose vertex and edge groups are infinite cyclic. Levitt proves that any generalized BaumslagSolitar group has property R∞, that is, any automorphism has an infinite number of twisted conjugacy classes. We show that any group quasi-isometric to a generalized Baumslag-Solitar group also has property R∞. This extends work of the authors proving that any group quasi-isometric to a solvable Baumslag-Solitar BS(1, n) group has property R∞, and relies on the classification of generalized Baumslag-Solitar groups given by Whyte.
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