For example, the action of any group on itself by left multiplication is free. This observation implies Cayley's theorem that any group can be embedded in a symmetric group (which is infinite when the group is). A finite group may act faithfully on a set of size much smaller than its cardinality (however such an action cannot be free). For instance the abelian 2-group (Z / 2 Z) (of cardinality 2) acts faithfully on a set of size 2 n. This is not always the case, for example the cyclic group Z / 2 Z cannot act faithfully on a set of size less than 2.