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

Abstract

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.

References in corpus (1)

• Twisted conjugacy classes of automorphisms of Baumslag-Solitar groups