"A Nice Way to See"
Logos
"Me — Thank you very much, Claude, for your perceptive remarks.
(By the way, I had in mind only the affine block actions
that make the conjecture work.) That's all for now.
Claude — Thinking about acknowledging previous mathematical
discussion clarification
Claude — You're welcome — and with the affine block actions,
your conjecture holds exactly as stated: those coset-permuting maps
across all choices of W generate precisely AGL(n,2). It's a nice way
to see the affine group built up from many overlapping S4's.
Glad I could help!"
Background reading . . .
"Binary Coordinate Systems," by Steven H. Cullinane —
http://finitegeometry.org/sc/gen/coord.html .
Quote adapted from a famous young-adult novel . . .
"There is such a thing as affine group generation
by permutation of parallel subspaces."