Question

THE FIRST ISOMORPHISM THEOREM Let: G M be a homomorphism with Ker() = K, and Im() = I. Then there is a natural isomorphism 0:1 ™G/K which is surjective. Thus, I G/K. THE SECOND ISOMORPHISM THEOREM Suppose the N is a normal subgroup of G, and that H is a subgroup of G. Then H/( HN) = (HN)/N. THE THIRD ISOMORPHISM THEOREM Let H and I be normal subgroups of G, and let N be a subgroup of H. Then (G/N)/(H/N) G/H

Can you explain these for me..I mean give example for each of them to get the idea

Answer 1

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