Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let $G$ be a finite group and $H<G, K<G$.

I have shown that $\left[G:H\cap K\right]\leq\left[G:H\right]\left[G:K\right]$

But I do not know where to begin to prove the equality in case these indexes are coprime.

I'd appreciate it much if a hint could be given.

share|improve this question
add comment

2 Answers

up vote 3 down vote accepted

Two hints:

1) $[G: H \cap K] = [G:H][H: H \cap K] = [G:K][K: H \cap K]$.
2) if $a \vert bc$ and $gcd(a,b) = 1$, then $a \vert c$.

share|improve this answer
That was VERY helpful.. thank you very much –  dankilman Nov 27 '11 at 17:05
add comment

I would first show that $[G:H \cap K] = [G:H] \cdot [H : H\cap K]$.

share|improve this answer
add comment

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.