Let $G$ a finite group and $H,K$ subgroups of $G$. Show that if $[G:H\cap K]= [G:H][G:K]$ then $G=HK$.
I proved that $G=HK$ implies $[G:H\cap K]= [G:H][G:K]$ but not the other direction.
Thanks for your help.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.Sign up to join this community