a) Prove that if a and b are elements of an Abelian group G, with o(a) = m and o(b) = n, then

.

b) With G, a, and b as in part (a), prove that o(ab) divides o(a)o(b).

c) Give an example of an Abelian group G and elements a and b in G such that o(ab)

o(a)o(b). Compare part (b)

I suspect I could figure out, or at least know where to start, part b if I knew part a (If t is an integer, then

iff n is a divisor of t)

But, I just don't know what to do with part a...

From what I understand,

and

I have done all sorts of random inserts of

,

, etc. Nothing seems to give me what I need though... erm, I was wondering, since

does

?