Context: Two groups G and H are called isomorphic if there exist group homomorphisms a: G → H and b: H → G, such that applying the two functions one after another in each of the two possible orders gives the identity functions of G and H. That is, a(b(h)) = h and b(a(g)) = g for any g in G and h in H. From an abstract point of view, isomorphic groups carry the same information. For example, proving that g • g = 1G for some element g of G is equivalent to proving that a(g) ∗ a(g) = 1H, because applying a to the first equality yields the second, and applying b to the second gives back the first.

Question: What are two groups called if they include homomorphisms?
Answer: isomorphic

Question: What similar element do isomorphic groups carry?
Answer: isomorphic groups

Question: How can showing the second equality yields the first prove the concept of isomorphic groups?
Answer: applying a to the first equality yields the second

Question: What are two groups called if no group homomorphisms are found?
Answer: Unanswerable

Question: Isomorphic groups carry different what?
Answer: Unanswerable

Question: What gives the identity of a?
Answer: Unanswerable

Question: From what point of view do isomorphic groups have different information?
Answer: Unanswerable

Question: How does the second equality disprove the concept of isomorphic groups?
Answer: Unanswerable