Question: Let n 2 be an integer, and let G1, G2, . . ., Gn be groups. For each i, let Ni be a subgroup of

Let n 2 be an integer, and let G1, G2, . . ., Gn be groups. For each i, let Ni be a subgroup of Gi .

A) Find necessary and sufficient conditions on the groups Ni so that N1 N2 Nn is a normal subgroup of G1 G2 Gn.

(B) Is it true that if M is a subgroup of G1 G2 Gn, then for each i there is a subgroup Ni of Gi so that M = N1 N2 Nn? Prove your answer.

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