Given normal subgroups <i>H</i> and <i>K</i> of <i>G</I>, we say that <i>G</i> is the internal direct product of <i>H</I> and <i>K</i> and write  
<i> H x K </i> if<br>
<br>
(1)<i> G = HK = {hk| h</i> belongs to <i>H</i> and <i>k</i> belongs to <i>K</i>}  and <br>
(2) <i> H</i> intersection <i> K</i> = {<i>e</i>}.