M Theory Lesson 249

To be definite, rather than turtles, let us pick the Weyl 1-circulant $(234 \cdots n1)$ all the way down through the prime factors of a number $n$. Then for the number $6$, the two possible permutations $P \in S_6$ are both of which satisfy $P^6 = 1$. For more than two prime factors for $n$, this process still selects a permutation satisfying $P^n = 1$, such as in this example for $12 = 3 \times 2 \times 2$. The product of an infinite number of prime factors would result in an infinite matrix.