Almost all permutations power to a cycle of prime length

Abstract

We show that almost all permutations have some power that is a cycle of prime length. The proof includes a theorem giving a strong upper bound on the proportion of elements of the symmetric group having no cycles with length in a given set.

6 pages. Precursor to preprint arXiv:1911.12613, by S.P. Glasby, Cheryl E. Praeger & W.R. Unger, "Most permutations power to a cycle of small prime length"