A conjecture of Glasby, Praeger, and Unger on permutations of $S_n$

Chiara Bellotti, Tim Trudgian

We prove a conjecture of Glasby, Praeger, and Unger concerning the symmetric group $S_n$. Let $\ddot{I}{€}_n$ denote the proportion of elements of $S_n$ that are pre-$p$-cycles for so…