There is a
remarkable correspondence between the 35 partitions of an
eight-element set H into two four-element sets and the 35 partitions of
the affine 4-space L over GF(2) into four parallel four-point planes.
Under this correspondence, two of the H-partitions have a common
refinement into 2-sets if and only if the same is true of the
corresponding L-partitions (Peter J. Cameron, *Parallelisms
of Complete Designs*, Cambridge U. Press, 1976, page 60). The
correspondence underlies the isomorphism* of the group A_{8}
with the projective general linear group PGL(4,2) and plays an
important role in the structure of the large Mathieu group M_{24}.

A 1954 paper by W.L. Edge suggests the correspondence should be named after E.H. Moore. Hence the title of this note.

Edge says that

It is natural to ask what,
if any, are the 8 objects which undergo

permutation. This question was discussed at length by
Moore…**.

But, while there is no thought either of controverting Moore's claim to

have answered it or of disputing his priority, the question is primarily

a geometrical one….

Excerpts from the Edge paper—

Excerpts from the Moore paper—

Pages 432, 433, 434, and 435, as well as the section mentioned above by Edge— pp. 438 and 439

* J.W.P. Hirschfeld, *Finite Projective Spaces of
Three Dimensions*, Oxford U. Press, 1985, p. 72

** Edge cited "E.H. Moore, *Math. Annalen*,
51 (1899), 417-44." A more complete citation from "The Scientific Work
of Eliakim Hastings Moore," by G.A. Bliss, *Bull.
Amer. Math. Soc.* Volume 40, Number 7 (1934),
501-514— E.H. Moore, "Concerning the General Equations of the
Seventh and Eighth Degrees," *Annalen*, vol. 51
(1899), pp. 417-444.