Question 5. (14 points) Suppose that : G→ H is a group homomorphism, K
5. (14 points) Suppose that : G→ H is a group homomorphism, K subgroup of G. 6. (14 points) Suppose A, B4G are normal subgroups such that AnB = {e}. Prove that if a EA and be B, then ab = ba. IMPORTANT: You should not simply quote the Proposition from class stating that AB Ax B. Instead, you should supply the first part of that proof of that proposition, stating that the elements of A commute with the elements of B.
subgroup of G. 6. (14 points) Suppose A, B4G are normal subgroups such that AnB = {e}. Prove that if a EA and be B, then ab = ba. IMPORTANT: You should not simply quote the Proposition from class stating that AB Ax B. Instead, you should supply the first part of that proof of that proposition, stating that the elements of A commute with the elements of B.
