subdirect product of groups (original) (raw)

Let (Gi)i∈I be a family of groups. A subgroup (http://planetmath.org/Subgroup) H of the direct product (http://planetmath.org/DirectProductAndRestrictedDirectProductOfGroups) ∏i∈IGiis said to be a subdirect product (or subcartesian product) of (Gi)i∈Iif πi⁢(H)=Gi for each i∈I, where πi:∏i∈IGi→Gi is the i-th projection map.