# CARMA Seminar

## Thursday, 17th Jul 2014

V206, Mathematics Building

# Simon Smith

(University of Western Australia)

# Infinite discrete primitive permutation groups

Usually, when we want to study permutation groups, we look first at the primitive permutation groups (transitive groups in which point stabilizers are maximal); in the finite case these groups are the basic building blocks from which all finite permutation groups are comprised. Thanks to the seminal O'Nan—Scott Theorem and the Classification of the Finite Simple Groups, the structure of finite primitive permutation groups is broadly known.

In this talk I'll describe a new theorem of mine which extends the O'Nan—Scott Theorem to a classification of all primitive permutation groups with finite point stabilizers. This theorem describes the structure of these groups in terms of finitely generated simple groups.