The product formula for Reidemeister numbers on nilpotent groups

2025/02/23 by Pieter Senden, Senden, Pieter · 1 citation
Mathematics · #20E45 #20F18 (Primary) 20E22 (Secondary) #Advanced Topics in Algebra #FOS: Mathematics #Graph theory and applications #Group Theory (math.GR) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2502.16651

openalex publication_date 2025/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the product formula for Reidemeister numbers on finitely generated torsion-free nilpotent groups in two ways. On the one hand, we generalise the product formula to central extensions. On the other hand, we derive general results for finitely generated (torsion-free) nilpotent groups from the product formula: we provide a strong tool to prove that an endomorphism on a finitely generated nilpotent group has infinite Reidemeister number and compute Reidemeister numbers on finite index subgroups of finitely generated torsion-free nilpotent groups. Using the latter, we provide an infinite family of groups with full Reidemeister spectrum.

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• Twisted conjugacy classes in Lie groups

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