external direct product of groups
The external direct product of two groups and is defined to be the set of ordered pairs , with and . The group operation is defined by
It can be shown that obeys the group axioms. More generally, we can define the external direct product of groups, in the obvious way. Let be the set of all ordered n-tuples and define the group operation by componentwise multiplication as before.
Title | external direct product of groups |
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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 product |
Related topic | CategoricalDirectProduct |
Related topic | DirectProductAndRestrictedDirectProductOfGroups |