For an arbitrary element A of a finite G form the sequence: A,A2,A3… 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 G form the sequence: A,A2,A3… 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 2π/3 in a tetrahedron, or the eight rotations by ±2π/3 in a cube.
