Log24

Tuesday, May 19, 2009

Tuesday May 19, 2009

Filed under: General,Geometry — Tags: , — m759 @ 7:20 PM
Exquisite Geometries

"By far the most important structure in design theory is the Steiner system S(5, 8, 24)."

"Block Designs," 1995, by Andries E. Brouwer

"The Steiner system S(5, 8, 24) is a set S of 759 eight-element subsets ('octads') of a twenty-four-element set T such that any five-element subset of T is contained in exactly one of the 759 octads. Its automorphism group is the large Mathieu group M24."

The Miracle Octad Generator (MOG) of R.T. Curtis (webpage)

"… in 1861 Mathieu… discovered five multiply transitive permutation groups…. In a little-known 1931 paper of Carmichael… they were first observed to be automorphism groups of exquisite finite geometries."

William M. Kantor, 1981

The 1931 paper of Carmichael is now available online from the publisher for $10.
 

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