---
title: "Orthomorphism"
chunk: 1/1
source: "https://en.wikipedia.org/wiki/Orthomorphism"
category: "reference"
tags: "science, encyclopedia"
date_saved: "2026-05-05T07:24:39.493560+00:00"
instance: "kb-cron"
---

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. Orthomorphisms and complete mappings are closely related.


== References ==