Kurt Gödel Research Center

2006 seminar talk: Nonstandard symmetric groups

Talk held by Richard Kaye (University of Birmingham) at the KGRC seminar on 2006-11-09.

Abstract

A nonstandard symmetric group is an internal finite symmetric group S_n inside a nonstandard model M of PA. This group can be considered internally as well as externally. Internally, it has a normal subgroup A_n of index 2, and A_n is simple for n>=5.

However, externally, A_n is an infinite group with an interesting normal subgroup structure. The main part of this talk will explain these normal subgroups of A_n. We conclude by examining interesting topological structures that can be imposed on these groups.

This is joint work with John Allsup, Birmingham.