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Finite Geometry of the Square and Cube

by Steven H. Cullinane

MSC 2000

20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures

51E20 Combinatorial structures in finite projective spaces

Abstract

The square and cube furnish convenient models of small finite geometries. Group actions on such models are discussed. There are applications to sporadic simple groups (via the "Miracle Octad Generator" of R. T. Curtis), to the connection between orthogonal Latin squares and projective spreads, and to symmetry of Walsh functions.