The question is: Let G be a finite group, H, K be normalsubgroups of G, and H?K is also a normal subgroup of G. UsingHomomorphism theorem ( or First Isomorphism theorem) prove thatG/(H?K) is isomorphism to a subgroup of(G/H)×(G/K). And give a example of group G withnormal subgroups H and K such that G/(H?K) ? (G/H)×(G/K), withexplanation.
I was trying to find some solutions for the isomorphism proofpart, but they all seems to have the condition with H?K = {e} . Ican ensure that there is no missing condition in my question. Asthere is another subquestion which I've already know the solution,is about given H?K = {e} and show G/(H?K) is isomorphism to(G/H)×(G/K).
