external direct product of groups

The external direct product G×H of two groups G and H is defined to be the set of ordered pairs (g,h), with gG and hH. The group operationMathworldPlanetmath is defined by


It can be shown that G×H obeys the group axioms. More generally, we can define the external direct product of n groups, in the obvious way. Let G=G1××Gn be the set of all ordered n-tuples {(g1,g2,gn)giGi} and define the group operation by componentwise multiplication as before.

Title external direct product of groups
Canonical name ExternalDirectProductOfGroups
Date of creation 2013-03-22 12:23:17
Last modified on 2013-03-22 12:23:17
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 8
Author mathcam (2727)
Entry type Definition
Classification msc 20K25
Synonym direct productMathworldPlanetmathPlanetmathPlanetmathPlanetmath
Related topic CategoricalDirectProduct
Related topic DirectProductAndRestrictedDirectProductOfGroups