Generating Sets of Cofinitary Groups
by
Bart Kastermans
University of Wisconsin --- Madison

Cofinitary groups are subgroups of the symmetric group on the natural numbers where all elements other than the identity have only finitely many fixed points. What the least complexity of maximal (w.r.t. inclusion) cofinitary groups are, is not determined yet. There are two similar results on the upper bounds, that motivated Anatoly Vershik to ask a question about computably generated groups: does there exist a group with a uniformly computable generating set whose isomorphism type is not computable. I will explain the motivation further and then talk about the positive answer to this question and ideas involved in the proof.

Date received: March 23, 2008