## Normal Subgroup of Product of Groups

In [6] it was formalized that the direct product of a family of groups gives a new group. In this article, we formalize that for all *j* ∈ *I*, the group *G* = Π_{i∈I}*G _{i}* has a normal subgroup isomorphic to

*G*. Moreover, we show some relations between a family of groups and its direct product.

_{j}
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