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1 results

  • 5 - Uniqueness of the Steiner System S(5, 8, 24) and the Group M24

  • Robert T. Curtis, University of Birmingham
  • Book:
    The Art of Working with the Mathieu Group M24
    Published online:
    31 October 2024
    Print publication:
    14 November 2024, pp 36-41

  • Summary

    A sextet is a partition of the 24 points of Ω into six tetrads such that the union of any two of them is an octad. We find all ways in which two sextets can intersect one another and use this knowledge to force any Steiner system S(5, 8, 24) to assume the form of the one given by the MOG. In so doing we show that if a Steiner system S(5, 8, 24) exists then the order of its group of automorphisms is 244, 823, 040 and that it acts quintuply transitively on the 24 points. That the MOG does define an S(5, 8, 24) was proved in Chapter 4.