(G;x) is a group ( e it's identity element). $\displaystyle H_1$ and $\displaystyle H_2$ are a subgroups from (G,x).

$\displaystyle H_1H_2$={$\displaystyle x_1x_2$/$\displaystyle (x_1;x_2$}$\displaystyle \in$ $\displaystyle H_1$x$\displaystyle H_2$}

1)-I must show that : $\displaystyle H_1H_2$ is a subgroup from(G;x) $\displaystyle \Longrightarrow H_1H_2=H_2H_1$

2)- We assume that $\displaystyle H_1$ and $\displaystyle H_2$ are finished and $\displaystyle H_1\cap H_2$={e} and:

$\displaystyle \phi$ : $\displaystyle H_1$x$\displaystyle H_2$ $\displaystyle \longrightarrow $$\displaystyle H_1$$\displaystyle H_2$

($\displaystyle x_1$;$\displaystyle x_2$)$\displaystyle \longrightarrow$ $\displaystyle x_1$$\displaystyle x_2$

I must show that $\displaystyle \phi$ is surjective and Card($\displaystyle H_1H_2$)=Card($\displaystyle H_1$)Card($\displaystyle H_2$)

I don't know anything!!!!!!! Can you give me some help please????