Almost all permutations power to a cycle of prime length
Group Theory
2019-12-03 v2
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.
Cite
@article{arxiv.1905.08936,
title = {Almost all permutations power to a cycle of prime length},
author = {William R. Unger},
journal= {arXiv preprint arXiv:1905.08936},
year = {2019}
}
Comments
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"