Some Involutions which Generate the Finite Symmetric Group

Abstract

Let $S_{n}$ be the symmetric group on $X_{n}=\{1, \dots, n\}$, for $n\geq 2$. In this paper we state some properties of subsemigroups generated by two involutions (a permutation with degree $2$) $\alpha,\beta$ such that $\alpha\beta$ is an $n$-cycle, and then state some generating sets of $S_n$ consists of involutions.