A classification of primitive permutation groups with finite stabilizers

TL;DR

This paper extends the Aschbacher-O'Nan-Scott Theorem to classify all infinite primitive permutation groups with finite point stabilizers, providing a comprehensive understanding of their structure.

Contribution

It offers a complete classification of infinite primitive permutation groups with finite stabilizers, expanding the foundational theorem to a broader class of groups.

Findings

Complete classification of infinite primitive groups with finite stabilizers

Extension of Aschbacher-O'Nan-Scott Theorem to new cases

Structural insights into primitive permutation groups

Abstract

We classify all infinite primitive permutation groups possessing a finite point stabilizer, thus extending the seminal Aschbacher-O'Nan-Scott Theorem to all primitive permutation groups with finite point stabilizers.