For an arbitrary element \(A\) of a finite \(\mathcal{G}\) form the sequence: \(A, A^{2}, A^{3} \ldots\) let the numbers of distinct elements in the sequence be \(p\). Thus we got the important result...For an arbitrary element \(A\) of a finite \(\mathcal{G}\) form the sequence: \(A, A^{2}, A^{3} \ldots\) let the numbers of distinct elements in the sequence be \(p\). Thus we got the important result that the order of a subgroup is a divisor of the order of the group. the three mirror planes of the regular triangle are in the same class and so are the four rotations by \(2 \pi / 3\) in a tetrahedron, or the eight rotations by \(\pm 2 \pi / 3\) in a cube.
