9 citations · 30 across the 13 of their papers we have counts for
13 papers
Taming Reidemeister zeta functions on virtually polycyclic groups
Sam Tertooy
We prove a formula for Reidemeister numbers of virtually polycyclic groups that generalises known formulas for finite groups and torsion-free virtually polycyclic groups. Based on…
A Hirsch length inequality
Sam Tertooy
Let and be subgroups of a virtually polycyclic group . We prove the Hirsch length inequality We show that equality holds when the num…
Class numbers and nilpotent subgroups of
Sam Tertooy
We show that for certain odd prime powers , the number of conjugacy classes of is greater than the order of its largest nilpotent subgroup. This answers nega…
Bi-twisted conjugacy in finite groups
Pieter Senden, Sam Tertooy
We provide two alternative ways to determine the number of bi-twisted conjugacy classes in a finite group: one using irreducible characters and one using ordinary conjugacy classes…
Algorithms for twisted conjugacy classes of polycyclic-by-finite groups II
Sam Tertooy
We construct an algorithm that, given a pair of homomorphisms between polycyclic-by-finite groups, determines whether their Reidemeister number is finite, and if so returns a set o…
Extreme Reidemeister spectra of finite groups
Sam Tertooy
We extend the notions of "-property" and "full (extended) Reidemeister spectrum" to finite groups in a meaningful way. We provide examples of finite groups admitting thes…
Twisted conjugacy and separability
Sam Tertooy
A group is twisted conjugacy separable if for every automorphism , distinct -twisted conjugacy classes can be separated in a finite quotient. Likewise, is completely…
Algorithms for twisted conjugacy classes of polycyclic-by-finite groups
Karel Dekimpe, Sam Tertooy
We construct two practical algorithms for twisted conjugacy classes of polycyclic-by-finite groups. The first algorithm determines whether two elements of a group are twisted conju…
The Reidemeister spectrum of low dimensional almost-crystallographic groups
Sam Tertooy
We determine which non-crystallographic, almost-crystallographic groups of dimension 4 have the -property. We then calculate the Reidemeister spectra of the 3-dimensional…
Reidemeister spectra for solvmanifolds in low dimensions
Karel Dekimpe, Sam Tertooy, Iris Van den Bussche
The Reidemeister number of an endomorphism of a group is the number of twisted conjugacy classes determined by that endomorphism. The collection of all Reidemeister numbers of all…
Fixed points of diffeomorphisms on nilmanifolds with a free nilpotent fundamental group
Karel Dekimpe, Sam Tertooy, Antonio R. Vargas
Let be a nilmanifold with a fundamental group which is free -step nilpotent on at least 4 generators. We will show that for any nonnegative integer there exists a self-d…
Reidemeister zeta functions of low-dimensional almost-crystallographic groups are rational
Karel Dekimpe, Sam Tertooy, Iris Van den Bussche
We prove that the Reidemeister zeta functions of automorphisms of crystallographic groups with diagonal holonomy are rational. As a result, we obtain that Reidemeist…
The Reidemeister spectra of low dimensional crystallographic groups
Karel Dekimpe, Tom Kaiser, Sam Tertooy
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 crystallog…