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The Steiner system S(5,8, 24) constructed from dual affine planes
Published online by Cambridge University Press: 14 November 2011
Synopsis
We construct firstly a single tactical configuration which has the structure of the dual of the affine plane of order 4, and show how to obtain a further set of 3 such dual planes which, together with , satisfy a certain set of intersection properties. This set of 4 dual planes is used to extend the 20 points of to the Steiner system = S(5, 8, 24). The construction leads to the production of involutions of the type which fix the points of an octad. It is shown that 3 involutions each of this type suffice to generate M24, each of the simple Mathieu groups inside M24, the Todd group, and all the intransitive maximal subgroups of M24.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 103 , Issue 1-2 , 1986 , pp. 147 - 160
- Copyright
- Copyright © Royal Society of Edinburgh 1986