TY - JOUR T1 - On the proportion of elements of order $2p$ in finite symmetric groups AU - Liu, Hailin AU - Zhong, Liping PY - 2025 DA - February DO - 10.15672/hujms.1367438 JF - Hacettepe Journal of Mathematics and Statistics PB - Hacettepe University WT - DergiPark SN - 2651-477X SP - 173 EP - 179 VL - 54 IS - 1 LA - en AB - This is one of a series of papers that aims to give an explicit upper bound on the proportion of elements of order a product of two primes in finite symmetric groups. This one presents such a bound for the elements with order twice a prime. KW - symmetric group KW - element KW - proportion KW - order CR - [1] S. Chowla, I. N. Herstein and W. R. Scott, The solutions of $x^d=1$ in symmetric groups, Norske Vid. Selsk. Forh. Trondheim 25, 29-31, 1952. CR - [2] S. P. Glasby, C. E. Praeger and W. R. Unger, Most permutations power to a cycle of small prime length, Proc. Edinburgh Math. Soc. 64, 234-246, 2021. CR - [3] E. Jacobsthal, Sur le nombre d’´el´ements du groupe sym´etrique Sn dont l’ordre est un nombre premier, Norske Vid. Selsk. Forh. Trondheim 21 (12), 49-51, 1949. CR - [4] L. Moser and M. Wyman, On solutions of $x^d=1$ in symmetric groups, Canad. J. Math. 7, 159-168, 1955. CR - [5] A. C. Niemeyer, T. Popiel and C. E. Praeger, On proportions of pre-involutions in finite classical groups, J. Algebra 324, 1016-1043, 2010. CR - [6] A. C. Niemeyer, C. E. Praeger and A. Seress, Estimation problems and randomised group algorithms, In Probabilistic Group Theory, Combinatorics and Computing, Editors: Alla Detinko, Dane Flannery and Eamonn O’Brien. Lecture Notes in Mathematics, Volume 2070 Chapter 2, 35-82 Springer, Berlin,2020. CR - [7] C. E. Praeger and E. Suleiman, On the proportion of elements of prime order in finite symmetric groups, Int. J. Group Theory 13, 251-256, 2024. UR - https://doi.org/10.15672/hujms.1367438 L1 - https://dergipark.org.tr/en/download/article-file/3438265 ER -