Semi-presentations for the sporadic simple groups

Abstract

A semi-presentation for a group $G$ is a set of relations which characterises a set of generators of $G$ up to automorphism. We discuss some techniques for finding semi-presentations and illustrate them by exhibiting semi-presentations on standard generators for the $26$ sporadic simple groups and their automorphism groups. We then show how these semi-presentations were used to check the data in the World Wide Web Atlas of Group Representations.