Almost all permutations power to a cycle of prime length

2019/05/22 by William R. Unger, Unger, William R. · 1 citation
Engineering · Computer Science · Mathematics · #graph theory and CDMA systems #Coding theory and cryptography #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.1905.08936

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.

Cited by

• A note on invariable generation of nonsolvable permutation groups

Related

• Counting pairs of cycles whose product is a permutation with restricted cycle lengths
• A Note on the Number of Permutations whose Cycle Lengths Are Prime\n Numbers
• The asymptotic of the number of permutations whose cycle lengths are prime numbers
• On the proportion of elements of prime order in finite symmetric groups
• The Cycle Structure of Permutations Without Long Cycles