Reidemeister numbers for arithmetic Borel subgroups in type A

2023/06/05 by Paula Macedo Lins de Araujo, de Araujo, Paula Macedo Lins, Yuri Santos Rêgo +1 · 1 citation
Mathematics · #20E36 #20F16 #20G30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2306.02936

openalex publication_date 2023/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Reidemeister number R(φ) of a group automorphism φ∈ Aut(G) encodes the number of orbits of the φ-twisted conjugation action of G on itself, and the Reidemeister spectrum of G is defined as the set of Reidemeister numbers of all of its automorphisms. We obtain a sufficient criterion for some groups of triangular matrices over integral domains to have property R_∞, which means that their Reidemeister spectrum equals \∞\. Using this criterion, we show that Reidemeister numbers for certain soluble S-arithmetic groups behave differently from their linear algebraic counterparts -- contrasting with results of Steinberg, Bhunia, and Bose.

Cited by

• Twisted conjugacy classes in Lie groups

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• The Reidemeister spectrum of ZM-groups
• Twisted conjugacy in soluble arithmetic groups
• The Reidemeister spectrum of finite abelian groups
• Reidemeister classes in lamplighter type groups
• The Reidemeister spectrum of split metacyclic groups