Twisted conjugacy classes in R. Thompson's group F

2007/04/25 by Collin Bleak, Alexander Fel’shtyn, Alexander Fel'shtyn +5 · 2 citations
Computer Science · Mathematics · #20E45 #37C25 #55M20 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #math.AT #math.GR #msc:20E45 #msc:37C25 #msc:55M20 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.0704.3411

10 pages

openalex publication_date 2007/04/25 · arxiv created 2007/05/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this short article, we prove that any automorphism of the R. Thompson's group F has infinitely many twisted conjugacy classes. The result follows from the work of Matthew Brin, together with a standard facts on R. Thompson's group F, and elementary properties of the Reidemeister numbers.

Cited by

• The Reidemeister spectrum of ZM-groups
• Geometry of Reidemeister classes and twisted Burnside theorem

Related

• Twisted conjugacy in Richard Thompson's group T
• Twisted conjugacy in generalized Thompson groups of type F
• The conjugacy problem in extensions of Thompson's group F
• Sigma theory and twisted conjugacy-II: Houghton groups and pure symmetric automorphism groups
• Twisted conjugacy classes in residually finite groups