# 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 SubdirectProductOfGroups 2013-03-22 14:53:25 2013-03-22 14:53:25 yark (2760) yark (2760) 7 yark (2760) Definition msc 20E26 subdirect product subcartesian product subcartesian product of groups ResiduallyCalP DirectProductAndRestrictedDirectProductOfGroups