Elementary amenable subgroups of R. Thompson's group F

Abstract

The subgroup structure of Thompson's group F is not yet fully understood. The group F is a subgroup of the group PL(I) of orientation preserving, piecewise linear self homeomorphisms of the unit interval and this larger group thus also has a poorly understood subgroup structure. It is reasonable to guess that F is the "only" subgroup of PL(I) that is not elementary amenable. In this paper, we explore the complexity of the elementary amenable subgroups of F in an attempt to understand the boundary between the elementary amenable subgroups and the non-elementary amenable. We construct an example of an elementary amenable subgroup up to class (height) omega squared, where omega is the first infinite ordinal.

20 pages

References in corpus (2)

• Automorphisms of generalized Thompson groups
• The ubiquity of Thompson's group F in groups of piecewise linear homeomorphisms of the unit interval

Cited by in corpus (3)

• Elementary totally disconnected locally compact groups
• A quasi-isometric embedding theorem for groups
• Dense normal subgroups and chief factors in locally compact groups