faithful group action
Let be a -set, that is, a set acted upon by a group with action. Then for any , the map defined by
is a permutation of (in other words, a bijective function from to itself) and so an element of .We can even get an homomorphism from to by the rule .
If for any pair we have, in other words, the homomorphism being injective, we say that the action is faithful
.