Generating the Mathieu groups and associated Steiner systems

✍ Scribed by Marston Conder

• Book ID: 103056952
• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 463 KB
• Volume: 112
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(93)90222-f

✦ Synopsis

Conder, M., Generating the Mathieu groups and associated Steiner systems, Discrete Mathematics 112 (1993) 41-47. With the aid of two coset diagrams which are easy to remember, it is shown how pairs of generators may be obtained for each of the Mathieu groups M,,, MIz, Mz2, M,, and Mz4, and also how it is then possible to use these generators to construct blocks of the associated Steiner systems S(4,5,1 l), S(5,6,12), S(3,6,22), S(4,7,23) and S(5,8,24) respectively. groups of degree 12 and 24 respectively, the point-stabilizers Ml1 and Mz3 are 4-transitive on 11 and 23 points respectively, and the stabilizer of two points in Mz4 is