The Reidemeister spectrum of direct products of nilpotent groups

TL;DR

This paper studies the Reidemeister spectrum of direct products of finitely generated torsion-free nilpotent groups, revealing how the spectra of factors determine the spectrum of the product through automorphism group analysis.

Contribution

It establishes that the Reidemeister spectrum of a direct product can be fully determined from the spectra of its factors under specific conditions, using automorphism group characterization.

Findings

Reidemeister spectra of factors determine the spectrum of the product.

Complete automorphism group of the direct product is determined.

Conditions for spectrum determination include torsion-free and indecomposable Malcev completion.

Abstract

We investigate the Reidemeister spectrum of direct products of nilpotent groups. More specifically, we prove that the Reidemeister spectra of the individual factors yield complete information for the Reidemeister spectrum of the direct product if all groups are finitely generated torsion-free nilpotent and have a directly indecomposable rational Malcev completion. We show this by determining the complete automorphism group of the direct product.