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Isomorphic proofs

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1.) G_1 is isomorphic to G_2 and H_1 is isomorphic to H_2 implies G_1/H_1 is isomorphic to G_2/H_2

2.) G_1 is isomorphic to G_2 and G_1/H_1 is isomorphic to G_2/H_2 implies H_1 is isomorphic to H_2

3.) H_1 is isomorphic to H_2 and G_1/H_1 is isomorphic to G_2/H_2 implies G_1 is isomorphic to G_2

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Solution Summary

This provides examples of completing proofs regarding isomorphisms.

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1. Answer : False
Counter Example: Let , , , then . But we note , . Therefore, is not isomorphic to .
2. Answer: True
Proof:
We ...

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