Semigroups with n-closed subsets (Q1117333)

A semigroup S is called n-closed iff \(M^ n\subseteq M\) for every subset \(M\subseteq S\). If S is 2-closed, then xy\(\in \{x,y\}\) for any \(x,y\in S\); every 3-closed semigroup is either 2-closed, a group of order two or a band, consisting of a 2-closed semigroup and a group of order two. Here it is shown that for any \(n>3\), if S is n-closed then S is also 3-closed.