On Veronese’s Decomposition Theorem and the Geometry of Outer Automorphisms of $S_6$

Abstract

In this paper, the Desargues Configuration in $P^2(k)$, where $k$ is a field of characteristic $\ne 2$, is characterized combinatorially en route to define Desargues Block Designs and associate them with certain families of dihedral subgroups of $S_6$ through the use of the outer automorphisms of $S_6$.