2005/01/06 by Matthew G. Brin, MATTHEW G. BRIN
Mathematics · #Advanced Operator Algebra Research #Class (philosophy) #Elementary theory #Finite Group Theory Research #Geometric and Algebraic Topology #Group (periodic table) #Locally finite group #Normal subgroup #Piecewise linear function #Stratification (seeds) #math.GR #msc:20E07 #msc:20E22 #msc:20F19 #msc:20F22
paper · pdf · doi:10.1142/s0218196705002517
20 pages
arxiv created 2005/01/06 · openalex publication_date 2005/08/01 · arxiv updated 2013/08/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study the subgroups of R. J. Thompson's group F and PL o (I), the group of orientation preserving, piecewise linear self homeomorphisms of [0, 1]. We exhibit, for each non-limit ordinal α ≤ ω 2 + 1, an elementary amenable group of elementary class α (under Chou's stratification of elementary amenable groups) that is a subgroup of F and thus of PL o (I). We also give examples that negatively answer a question of Sapir about non-solvable groups in F and PL o (I).