2006 seminar talk: Nonstandard symmetric groups
Talk held by Richard Kaye (University of Birmingham) at the KGRC seminar on 2006-11-09.
A nonstandard symmetric group is an internal finite symmetric group Sn inside a nonstandard model M of PA. This group can be considered internally as well as externally. Internally, it has a normal subgroup An of index 2, and An is simple for n>=5.
However, externally, An is an infinite group with an interesting normal subgroup structure. The main part of this talk will explain these normal subgroups of An. We conclude by examining interesting topological structures that can be imposed on these groups.
This is joint work with John Allsup, Birmingham.