A note on twisted conjugacy and generalized Baumslag-Solitar groups

Details A note on twisted conjugacy and generalized Baumslag-Solitar groups A note on twisted conjugacy and generalized Baumslag-Solitar groups

2006-06-12

arxiv.org/abs/math/0606284v3

Mathematics

Group Theory

8 pages

Scientific paper

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 Baumslag-Solitar group has property R-infinity, 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-infinity. This extends work of the authors proving that any group quasi-isometric to a solvable Baumslag-Solitar BS(1,n) group has property R-infinity, and relies on the classification of generalized Baumslag-Solitar groups given by Whyte.

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