The $R_{\infty }$ property for free groups, free nilpotent groups and free solvable groups

Abstract

Let $F$ be either a free nilpotent group of a given class and of finite rank or a free solvable group of a certain derived length and of finite rank. We show precisely which ones have the $R_{\infty }$ property. Finally, we also show that the free group of infinite rank does not have the $R_{\infty }$ property.

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• Structure and automorphisms of pure virtual twin groups
• Twisted Burnside-Frobenius theory for endomorphisms of polycyclic groups
• Twisted Conjugacy in Direct Products of Groups
• The $R_{\infty }$-property for right-angled Artin groups
• Some remarks on twin groups
• Fixed points of diffeomorphisms on nilmanifolds with a free nilpotent fundamental group
• Reidemeister spectra for solvmanifolds in low dimensions
• Twisted conjugacy in soluble arithmetic groups
• Reidemeister classes in some weakly branch groups
• The R${}_{\infty }$ property for pure Artin braid groups
• The Reidemeister spectrum of ZM-groups