subdirect product of groups

Let $(G_{i})_{i\in I}$ be a family of groups. A subgroup (http://planetmath.org/Subgroup) $H$ of the direct product (http://planetmath.org/DirectProductAndRestrictedDirectProductOfGroups) $\prod_{i\in I}G_{i}$ is said to be a subdirect product (or subcartesian product) of $(G_{i})_{i\in I}$ if $\pi_{i}(H)=G_{i}$ for each $i\in I$ , where $\pi_{i}\colon\prod_{i\in I}G_{i}\to G_{i}$ is the $i$ -th projection map.

Title	subdirect product of groups
Canonical name	SubdirectProductOfGroups
Date of creation	2013-03-22 14:53:25
Last modified on	2013-03-22 14:53:25
Owner	yark (2760)
Last modified by	yark (2760)
Numerical id	7
Author	yark (2760)
Entry type	Definition
Classification	msc 20E26
Synonym	subdirect product
Synonym	subcartesian product
Synonym	subcartesian product of groups
Related topic	ResiduallyCalP
Related topic	DirectProductAndRestrictedDirectProductOfGroups