Algebra Seminar: Reid -- Commensurators of free groups and free pro-p groups

Colin Reid (Western Sydney University) will be speaking in the algebra seminar.  We will
go out for lunch after the talk---all are welcome to join! 

When: 12-1pm Friday September 12 

Where: Carslaw 175 

Title: Commensurators of free groups and free pro-p groups 

Abstract: (Joint work with Y.  Barnea, M.  Ershov, A.  Le Boudec, M.  Vannacci and Th.
Weigel.)  The commensurator of a group G is a group that encapsulates (up to a suitable
equivalence) all isomorphisms between finite index subgroups of G.  We study the
commensurator of a free group F and of a free pro-p group, and also the p-commensurator
of F (the subgroup of the commensurator that respects the pro-p topology on F), with a
focus on normal subgroup structure; the p-commensurator turns out to have a simple
subgroup of index at most 2.  As well as 'global' results about the commensurator as a
whole, we obtain some new constructions of simple groups: finitely generated simple
groups with a free commensurated subgroup, and compactly generated simple locally
compact groups that have an infinite pro-p open subgroup, possibly free pro-p.