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Monday, July 29, 2013

St. Walter’s Day

Filed under: General,Geometry — m759 @ 5:05 PM

Today is the dies natalis  of group theorist  Walter Feit.

     "The Steiner systems (5,6,12) and (5,8,24) are remarkable combinatorial
configurations unlike any others. Their automorphism groups are the Mathieu
groups M12 and M24. These are the only 5-transitive permutation groups other
than symmetric and alternating groups: (a fact long conjectured but only
proved as a consequence of the classification). The Leech lattice is a blown up
version of (5,8,24).
It is the unique even unimodular lattice in 24 dimensions
with no vectors of weight 2. This uniqueness is an essential reason why it is a
geometric object of fundamental importance. The automorphism group Co.O
of the Leech lattice involves about half of the sporadic groups and generally it
is felt that these are well understood."

— Walter Feit, book review, Bulletin of the American Mathematical Society ,
     Vol. 8 (1983), 120-124, page 123

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