For normal subgroups  <i>H<sub>1</sub>,  H<sub>2</sub>,..., H<sub>n</sub></i>    
 <i>G</i> is the internal direct product  <i>H<sub>1</sub> x H<sub>2</sub> x...xH<sub>n</sub></i> if <br>
<br>

(1) <i>G = H<sub>1</sub>H<sub>2</sub>...H<sub>n</sub></i>   and<br>
(2)   the intersection of 
<i> H<sub>1</sub>H<sub>2</sub>...H<sub>i</sub></i>   and <i>H<sub>i +1</sub> = {e}</i> for <i>i = 1, 2,..., n-1</i>.