The $R_{\infty }$--property for nilpotent quotients of Baumslag--Solitar groups

Abstract

A group $G$ has the $R_{\infty }$--property if the number $R(\phi )$ of twisted conjugacy classes is infinite for any automorphism $\phi$ of $G$. For such a group $G$, the $R_{\infty }$--nilpotency index is the least integer $c$ such that $G/{\gamma }_{c+1}(G)$ still has the $R_{\infty }$--property. In this paper, we determine the $R_{\infty }$--nilpotency degree of all Baumslag--Solitar groups.

12 pg

References in corpus (1)

• On the automorphism group of generalized Baumslag-Solitar groups