  The reality of the difficulties in investigation of finite groups are
considered. It is shown that the consideration of symmetry properties of the
$k$-orbits that are obtained with an action of a finite group $F=(V,\cdot)$ on
Cartesian power $V^k$ gives a new view on the nature of groups and simplifies
some difficult properties of groups.
  Using this representation it is obtained a simple proof of the W. Feit, J.G.
Thompson theorem: Solvability of groups of odd order.
