Elementary amenable subgroups of R. Thompson's group F

Details Elementary amenable subgroups of R. Thompson's group F Elementary amenable subgroups of R. Thompson's group F

2005-01-06

arxiv.org/abs/math/0501085v1

Mathematics

Group Theory

20 pages

Scientific paper

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.

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