Direct product of subgroups of factors in direct product decomposition into cyclic groups

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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

Definition

Suppose G is a finitely generated abelian group. A subgroup H of G is termed a direct product of subgroups of factors in direct product decomposition into cyclic groups if there exists a decomposition of G as an internal direct product of cyclic groups:

G = G_1 \times G_2 \times \dots \times G_n

and subgroups H_i \le G_i such that:

H = H_1 \times H_2 \times \dots \times H_n