A group <i>G</I>  is  solvable group if it has a series of subgroups<br>
{<i>e</i>} =
<i>H<sub>1</sub> &#8834 H<sub>2</sub> &#8834  &#8230 &#8834 H<sub>k</sub> = G</i>,  where for each 0 &#8804 <I> i < k</i>,
<i>H<sub>i</sub></I>  is normal in
 <i>H<sub>i + 1</sub></i> and
 <i>H<sub>i + 1</sub>/H<sub>i</sub></i>  is Abelian.