Any map f : (G, o) ---> (G', o') is called homomorphism if

1
f (x o y) = f(x) o' f(y)
2
f (x o y) = f(y) o' f(x)
3
f (x o' y) = f(x) o f(y)
4
f (x o' y) = f(x) o' f(y)

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