# Isomorphic proofs

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

© BrainMass Inc. brainmass.com October 9, 2019, 10:44 pm ad1c9bdddfhttps://brainmass.com/math/discrete-math/isomorphic-proofs-230516

#### Solution Preview

1. Answer : False

Counter Example: Let , , , then . But we note , . Therefore, is not isomorphic to .

2. Answer: True

Proof:

We ...

#### Solution Summary

This provides examples of completing proofs regarding isomorphisms.

$2.19