If and , , show that the order of in divides .

So I know that and will ? From Lagrange's theorem K|G?

Thanks guys

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- Nov 7th 2009, 12:58 PMsfspitfire23Factor group order
If and , , show that the order of in divides .

So I know that and will ? From Lagrange's theorem K|G?

Thanks guys - Nov 7th 2009, 01:10 PMtonio
- Nov 7th 2009, 03:45 PMalunw
I'm confused about your claim in the second part of your second lemma.

Let G be the group of integers under addition and H the integers modulo n under addition. That is surely a homomorphism that is sending torsion free elements to elements with finite order that are not the identity. Am I misunderstanding your notation? - Nov 7th 2009, 04:35 PMtonio
- Nov 8th 2009, 03:15 PMsfspitfire23
What I have-

For any element g in G defines the right coset of K. Each k in K will have a different product when multiplied by any g. Thus, each element of K will create a corresponding unique element of Kg. So, Kg will have the same number of elements as K (same order as K). Now, the order of K will be and the order of G is . They each produce the identity element and thus divide each other.....?