"Let G be the group generatied by … arbitrarily mixing random
permutations of rows and of columns with random permutations
of the four 2×2 quadrants…. G is isomorphic to the affine group
on V4 (GF(2))." — Steven H. Cullinane, October 1978.
Compare and contrast with another discussion of randomness and
affine groups, from American Mathematical Monthly, November 1995 —
Related material not cited by Poole in 1995 —
J. E. Johnson, "Markov-type Lie groups in GL(n, R),"
J. Math. Phys. 26, 252-257 (1985).
The above Johnson citation is from an article that also discusses
the work of Poole —
Irene Paniello, "On Actions on Cubic Stochastic Matrices,"
arXiv preprint dated April 22, 2017. Published in
Markov Processes and Related Fields, 2017, v.23, Issue 2, 325-348.
