Reidemeister spectrum for metabelian groups of the form Qⁿ\rtimes \mathbb Z and \mathbb Z[1/p]ⁿ\rtimes \mathbb Z, p prime

2009/09/17 by Alexander Fel’shtyn, Fel'shtyn, Alexander, Daciberg Lima Gonçalves +1
Mathematics · #20E45 #37C25 #55M20 #Advanced Algebra and Geometry #Algebraic Topology (math.AT) #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.0909.3128

openalex publication_date 2009/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we study the Reidemeister spectrum for metabelian groups of the form \mathbb Qⁿ\rtimes \mathbb Z and \mathbb Z[1/p]ⁿ\rtimes \mathbb Z. Particular attention is given to the R_∞ property of a subfamily of these groups. We also define a Nielsen spectrum of a space and discuss some examples.

Related

• On the Reidemeister spectrum and the R_∞ property for some free nilpotent groups
• The Reidemeister spectrum of split metacyclic groups
• Extreme Reidemeister spectra of finite groups
• The Reidemeister spectrum of ZM-groups
• Reidemeister numbers for arithmetic Borel subgroups in type A