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Journal of the London Mathematical Society Advance Access originally published online on July 14, 2007
Journal of the London Mathematical Society 2007 75(3):705-717; doi:10.1112/jlms/jdm024
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© 2007 London Mathematical Society

Twisted conjugacy and quasi-isometry invariance for generalized solvable Baumslag–Solitar groups

Jennifer Taback1 and Peter Wong2,

1 Department of Mathematics
Bowdoin College
Brunswick, ME 04011
USA
jtaback{at}bowdoin.edu
2 Department of Mathematics
Bates College
Lewiston, ME 04240
USA

We say that a group has property R{infty} if any group automorphism has an infinite number of twisted conjugacy classes. Fel'shtyn and Gonçalves proved that the solvable Baumslag-Solitar groups BS(1, m) have property R{infty}. We define a solvable generalization {Gamma}(S) of these groups which is shown to have property R{infty}. It is also shown that property R{infty} is geometric for these groups, that is, any group quasi-isometric to {Gamma}(S) has property R{infty} as well.

pwong{at}bates.edu

2000 Mathematics Subject Classification 20E45 (primary), 20E08, 20F65, 55M20 (secondary).

The first author acknowledges support from NSF grant DMS-0437481 and would like to thank Kevin Whyte for many useful conversations about this paper. We thank the referee for helpful comments.

Received January 11, 2006; revised July 25, 2006; published online July 14, 2007.


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