- #1
lola1990
- 30
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Homework Statement
Let H be a subgroup of K and K be a subgroup of G. Prove that |G|=|G:K||K|. Do not assume that G is finite
Homework Equations
|G|=|G/H|, the order of the quotient group of H in G. This is the number of left cosets of H in G.
The Attempt at a Solution
I would use LaGrange's Thm, but G is not necessarily finite. I thought a good idea would be to try to find an isomorphism from G/K x K/H to G/H. I defined A(aK x bH)=abH, but I am having trouble proving it is an isomorphism (not even sure it is one!). Is this the right approach? If not, what would be a better way?