Transporter

Let $M$ be a monoid operating on a set $S$ , and let $A$ and $B$ be subsets of $S$ . Then the transporter of $A$ to $B$ is the set of elements $a\in M$ for which $a(A) \subseteq B$ . The strict transporter of $A$ to $B$ is the set of $a\in M$ for which $a(A) = B$ . The transporter of $A$ to itself is called the stabilizer of $A$ .