# Math Help - sub-groups

1. ## sub-groups

Is $G$ a finite group , $H$ $,$ $K$ subgroups such that $H K$.
Prove $[ G:H ] = [ G:K ] . [ K:H ]$

Please can develop it in detail.

THANKS YOU FRIENDS....

2. Its just a simple application of Lagrange:

$[G:H]=\frac{ \vert G \vert }{ \vert H \vert }$ and $\vert H \vert = \frac{ \vert K \vert }{ [K:H] }$ substitute in the first and you get $[G:H] = \frac{ \vert G \vert }{ \vert K \vert } [K:H] = [G:K][K:H]$

3. ## help

thanks for the help, that I needed to think a bit