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

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

2006-01-12

arxiv.org/abs/math/0601271v2

J. Lond. Math. Soc. (2) 75 (2007), no. 3, 705--717

Mathematics

Group Theory

Scientific paper

We say that a group has property $R_{\infty}$ if any group automorphism has an infinite number of twisted conjugacy classes. Fel'shtyn and Goncalves prove that the solvable Baumslag-Solitar groups BS(1,m) have property $R_{\infty}$. We define a solvable generalization $\Gamma(S)$ of these groups which we show to have property $R_{\infty}$. We then show that property $R_{\infty}$ is geometric for these groups, that is, any group quasi-isometric to $\Gamma(S)$ has property $R_{\infty}$ as well.

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