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Prove that if A is a subgroup of G and B is a subgroup of H,...

Prove that if A is a subgroup of G and B is a subgroup of H, then the direct product A × B is a subgroup of G × H.

Show all steps. Note that AXB is nonempty since the identity e is a part of A X B. Remains only to show that A X B is closed under multiplication and inverses.

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