# Crossed modules

From Encyclopedia of Mathematics

A concept arising from the concept of a -module (see Module). A group (not necessarily Abelian) with a group of operators and homomorphism such that for any and all ,

is called a crossed -module. is a -module (i.e. its underlying group is Abelian) if and only if ().

**How to Cite This Entry:**

Crossed modules.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Crossed_modules&oldid=11880

This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article