Definition:Direct Sum of Groups

Definition
Let $I$ be a indexing set.

Let $(G_i)_{i \in I}$ be a family of groups.

The direct sum of $(G_i)_{i \in I}$ is the subgroup of their direct product consisting of mappings of finite support.

Also see

 * Direct Sum of Groups is Subgroup of Direct Product
 * Definition:Coproduct of Groups
 * Definition:Direct Sum of Topological Groups