AUTOMORPHISM

in mathematics, an assignment that associates to every element in a set one and only one other element (perhaps itself) and for which there is a companion assignment such that one assignment followed by the other produces the assignment in which every element is associated with itself. Furthermore, operations such as addition and multiplication, if they exist, must be preserved; for example, if s (a) is the element associated to a, then s (a + b) = s (a) + s (b) and s (ab) = s (a)s (b) for any a, b.