(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let H and K be subgroups of a finite group G with coprime indices. Prove that G=HK

2. Relevant equations

From a theorem we have, If |G| and |G:K| are finite and coprime, we have:

|G intersect K|=|G|*|G:K|

|G| indicates the index of G over H, not the order here...a notational point that hurts my head.

3. The attempt at a solution

I used the thoerem and I got

|G intersect K|=|G|*|G:K|

but since G and H are of coprime index, (H intersect K=1),

So that I get

|G|=|G|*|G:K|

if I let |G|=p and |G:K|=q then |G|=pq

That's where I am and I don't think I'm headed in the right direction.

pointers and clarification will be greatly appreciated.

CC

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# Homework Help: Group theory

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