The Reidemeister spectra of low dimensional crystallographic groups

Abstract

In this paper we study the number of twisted conjugacy classes (the Reidemeister number) for automorphisms of crystallographic groups. We present two main algorithms for crystallographic groups whose holonomy group has finite normaliser in ${\mathrm{GL}}_n(\mathbb{Z})$. The first algorithm calculates whether a group has the $R_{\infty }$-property; the second calculates the Reidemeister spectrum. We apply these algorithms to crystallographic groups up to dimension $6$.

19 pages

References in corpus (1)

• Reidemeister spectra for solvmanifolds in low dimensions

Cited by in corpus (8)

• Twisted Conjugacy in Direct Products of Groups
• Reidemeister zeta functions of low-dimensional almost-crystallographic groups are rational
• The Reidemeister spectrum of low dimensional almost-crystallographic groups
• Twisted conjugacy in soluble arithmetic groups
• Algorithms for twisted conjugacy classes of polycyclic-by-finite groups
• Characteristic subgroups and the R${}_{\infty }$-property for virtual braid groups
• The Reidemeister spectrum of ZM-groups
• The Reidemeister spectrum of split metacyclic groups