Orthomorphism
In abstract algebra, an orthomorphism is a certain kind of mapping from a group into itself. Let G be a group, and let θ be a permutation of G. Then θ is an orthomorphism of G if the mapping f defined by f(x) = x−1 θ(x) is also a permutation of G. A permutation φ of G is a complete mapping if the mapping g defined by g(x) = xφ(x) is also a permutation of G.[http://mathworld.wolfram.com/Orthomorphism.html Orthomorphism – Mathworld] Orthomorphisms and complete mappings are closely related.{{citation|first1=J.|last1=Denes|first2=A.D.|last2=Keedwell|title=Latin Squares and their Applications|year=1974|publisher=Academic Press|isbn=0-12-209350-X|page=232}}