Crossed modules

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