Abstract Let ${\mathbb{P}}(ord\pi = ord\pi ')$ be the probability that two independent, uniformly random permutations of [ n ] have same order. Answering a question Thibault Godin, we prove ') {n^{ - 2 + o(1)}}$ and \ge {1 \over 2}{n^{ 2}}lg*n$ for infinitely many . (Here lg * is height tallest tower twos less than or equal to .)
