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Two groups are isomorphic if and only if __________ is existed between them.

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Two groups are isomorphic if and only if __________ is existed between them.

(a) homomorphism

(b) endomorphism

(c) isomorphism

(d) association

I had been asked this question in quiz.

My question is from Groups topic in portion Groups of Discrete Mathematics

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The correct option is (c) isomorphism

Best explanation: Two groups M and K are isomorphic (M ~= K) if and only if there exists an isomorphism between them. An isomorphism f:M -> K between two groups M and K is a mapping which satisfies two conditions: 1) f is a bijection and 2) for every x,y belongs to M, we have f(x*My) = f(x) * Kf(y).

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