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# 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.[1] Orthomorphisms and complete mappings are closely related. [2]

References

Orthomorphism – Mathworld

Denes, J.; Keedwell, A.D. (1974), Latin Squares and their Applications, Academic Press, p. 232, ISBN 0-12-209350-X

Undergraduate Texts in Mathematics

Graduate Studies in Mathematics

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