Simple Groups of Order Less than 10000

Abstract

This is another ‘descriptive’ chapter giving an account of simple groups with order less than 10000. We introduce Steiner systems—their automorphisms provide a new way to construct groups, prove the simplicity of the linear (matrix) groups L _n (q), and discuss one ‘classical’ (U ₃(3), a unitary group) and one ‘sporadic’ (M ₁₁, the first Mathieu group) group in detail. Some numerical data is also given but many proofs are omitted. Appendix E, see page 295, gives data on the groups L ₂(q), and an appendix at Web Section 12.6 provides more information about Steiner systems for Mathieu groups, revisits the simplicity of the groups L _n (q), and data on simple groups of order less than 10⁶.