Hi,

So... I've decided to study some algebra, to see if I can handle it... lol

I've come accross this (very basic) question, which may rather be set theory, but the original question is algebra :

Let G be a group. Let H be a subgroup containing a subset P.

Prove that $\displaystyle \langle P\rangle_H=\langle P\rangle_G$

So basically, I have to prove that $\displaystyle \bigcap_{I\in\mathcal{I}} I=\bigcap_{H\in\mathcal{H}} H$

Where $\displaystyle \mathcal{I}=\{\text{subgroups of H containing P}\}$ and $\displaystyle \mathcal{H}=\{\text{subgroups of G containing P}\}$

It is clear that $\displaystyle \mathcal{I}\subseteq \mathcal{H}$

So it is very logical to have the equality $\displaystyle \bigcap_{I\in\mathcal{I}} I=\bigcap_{H\in\mathcal{H}} H$

But I didn't succeed in finding a formal proof

Thanks,