On idempotent generated semigroups (Q1611025)

Let \(X=\{1,2,\dots,n\}\) and let \(T_n\) and \(S_n\) denote, respectively, the full transformation semigroup on \(X\) and the symmetric group on \(X\). Let \(I_n=T_n\setminus S_n\) and for \(t\in I_n\), let \(C_t=\{g^{-1}tg:g\in S_n\}\) and let \(t^{S_n}=\langle\{t\}\cup S_n\rangle\setminus S_n\). The author proves, among other things, that if \(e\) is an idempotent in \(I_n\) and \(g\in S_n\), then \(\langle C_e\rangle=e^{S_n}=(eg)^{S_n}\).