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**knguyen2005** Let G be a group and x belongs to G,

Define ord(x) = min{r >= 1 : x^r = 1}

If f: G map to H is an injective group homomorphism. Show that, for

each x in G, ord(f(x)) = ord(x).

I think I come up with the approach is that , I need to show that

ord(f(x)) divides r and hence the result is proved.

Or: I can somehow show that ord(f(x)) = min{ r >= 1 : (f(x))^r = 1} which is by the definition.

Can you tell me whether the above approaches are right or wrong, if they are wrong then show me how to solve this question please?