Finite index subgroups of R. Thompson's group F

2007/11/07 by Collin Bleak, Bleak, Collin, Bronlyn Wassink +1
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #20F60 #FOS: Mathematics #Fluorine in Organic Chemistry #General Topology (math.GN) #Group Theory (math.GR) #math.GN #math.GR #msc:20F60

paper · pdf · doi:10.48550/arxiv.0711.1014

26 pages, 8 figures

arxiv created 2007/11/07 · openalex publication_date 2007/11/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The authors classify the finite index subgroups of R. Thompson's group F. All such groups that are not isomorphic to F are non-split extensions of finite cyclic groups by F. The classification describes precisely which finite index subgroups of F are isomorphic to F, and also separates the isomorphism classes of the finite index subgroups of F which are not isomorphic to F from each other; characterizing the structure of the extensions using properties of the structure of the finite index subgroups of Z× Z.

Related

• On subgroups of R. Thompson's group F
• On some generating set of Thompson's group F
• Subgroups of R. Thompson's Group F that are Isomorphic to F
• On the stabilizers of finite sets of numbers in the R. Thompson group\n F
• Quasi-isometrically embedded subgroups of Thompson's group F