A Lower Bound of Conjugacy Class Length of Symmetric Group

Abstract

In this paper, an inequality is proved and using this inequality, we obtain a lower bound of all conjugacy class lengths of Sn, where Sn is a symmetric group of degree n, n ≥ 3. Further using another inequality, we get a lower bound (only depend on n) of some conjugacy class lengths of symmetric group Sn, n ≥ 15.