kb/data/en.wikipedia.org/wiki/Orthomorphism-0.md

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