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**chocaholic** Let G,G' be groups and φ:G-->G' be a homomorphism. Then prove:

a)if o(g)=n ,then o(φ(g))|n

b)if o(g)=n and φ is injective, then o(φ(g))=n

Firstly I don't actually understand the question. What does the o mean?Is it a new mapping which hasn't been defined or does it represent the composition of functions and if so then how is it computed?Secondly does the |n in (a) represent "divides n" and if so how is that proved, if not then what does it represent? Neither of these appears in my abstract algebra text. In (b) I know that an injective function is one to one but again I don't really understand the question.

Any help would be greatly appreciated. Thanks in advance.