ELEMENTARY AMENABLE SUBGROUPS OF R. THOMPSON'S GROUP F

Abstract

We study the subgroups of R. J. Thompson's group F and PLo(I), the group of orientation preserving, piecewise linear self homeomorphisms of [0, 1]. We exhibit, for each non-limit ordinal α ≤ ω2 + 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 PLo(I). We also give examples that negatively answer a question of Sapir about non-solvable groups in F and PLo(I).