Transitive permutation groups with trivial four point stabilizers

TL;DR

This paper classifies transitive permutation groups with trivial four point stabilizers, focusing on simple and quasisimple groups, motivated by automorphisms of Riemann surfaces and Weierstrass points.

Contribution

It provides a complete classification of such groups when they are simple or quasisimple, advancing understanding of their structure.

Findings

Classification of simple and quasisimple groups with trivial four point stabilizers

Insights into automorphisms of Riemann surfaces and Weierstrass points

Extension of previous work on permutation group structures

Abstract

In this paper we analyze the structure of transitive permutation groups that have trivial four point stabilizers, but some nontrivial three point stabilizer. In particular we give a complete, detailed classification when the group is simple or quasisimple. This paper is motivated by questions concerning the relationship between fixed points of automorphisms of Riemann surfaces and Weierstrass points and is a continuation of the authors' earlier work.