A universal, minimal, non-solvable subgroup of PLo(I) and of R. Thompson's Group F
by
Collin Bleak
Binghamton University

There has been research into the question of whether the group PL_o(I) (piecewise-linear, orientation preserving homeomorphisms of the unit interval under the operation of composition) admits a universal minimal non-solvable subgroup. We will outline an argument which demonstrates that the answer to this is "Yes." We give a description of this group W, and we note the following two corollaries; first, R. Thompson's group F also contains a copy of W as a universal minimal non-solvable subgroup, and second, given any non-solvable subgroup N of PL_o(I) or F, and any solvable subgroup S of PL_o(I) or F, we have that S embeds in N.

Date received: March 20, 2006