Twisted conjugacy classes in nilpotent groups

Abstract

Let $N$ be a finitely generated nilpotent group. Algorithm is constructed such, that for every automorphism $\varphi \in Aut(N)$ defines the Reidemeister number $R(\varphi ).$ It is proved that any free nilpotent group of rank $r=2$ or $r=3$ and class $c\ge 4r,$ or rank $r\ge 4$ and class $c\ge 2r,$ belongs to the class $R_{\infty }.$

8 pages

References in corpus (2)

• A note on twisted conjugacy and generalized Baumslag-Solitar groups
• The geometry of twisted conjugacy classes in wreath products

Cited by in corpus (3)

• On the Reidemeister spectrum and the $R_{\infty }$ property for some free nilpotent groups
• Limits of Baumslag-Solitar groups and dimension estimates in the space of marked groups
• Reidemeister spectrum for metabelian groups of the form $Q^n⋊\mathbb{Z}$ and ${\mathbb{Z}[1/p]}^n⋊\mathbb{Z}$, $p$ prime