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Find an abelian group (G,+) and its three subgroups, G1, G2,G3 such as Gi ∩ Gj...

Find an abelian group (G,+) and its three subgroups, G1, G2,G3 such as Gi ∩ Gj = {0}, for i, j, and  G = G1 + G2 + G3 is NOT the direct product of
G1, G2, G3. Also consider whether the Z30 is the direct product of of the subgroups <6¯>, <10¯>, <15¯>.

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