TY - UNPB
T1 - On the proportion of elements of prime order in finite symmetric groups
AU - Praeger, C.E.
AU - Suleiman, E.
PY - 2022/10/27
Y1 - 2022/10/27
N2 - We give a short proof for an explicit upper bound on the proportion of permutations of a given prime order p, acting on a set of given size n, which is sharp for certain n and p. Namely, we prove that if n ≡ k (mod p) with 0 ≤ k ≤ p−1, then this proportion is at most (p · k!)−1 with equality if and only if p ≤ n < 2n.
AB - We give a short proof for an explicit upper bound on the proportion of permutations of a given prime order p, acting on a set of given size n, which is sharp for certain n and p. Namely, we prove that if n ≡ k (mod p) with 0 ≤ k ≤ p−1, then this proportion is at most (p · k!)−1 with equality if and only if p ≤ n < 2n.
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85141577779&partnerID=MN8TOARS
U2 - 10.48550/arXiv.2210.15355
DO - 10.48550/arXiv.2210.15355
M3 - Preprint
T3 - International Journal of Group Theory
SP - 251
EP - 256
BT - On the proportion of elements of prime order in finite symmetric groups
PB - arXiv
ER -