Cyclic group:Z6

Verbal definition
The cyclic group of order 6 is defined as the group of order six generated by a single element. Equivalently it can be described as a group with six elements $$e= x^0,x,x^2,x^3,x^4,x^5$$ where $$x^lx^m = x^{l+m}$$ with the exponent reduced mod 3. It can also be viewed as:


 * The quotient group of the group of integers by the subgroup of multiples of 6.
 * The multiplicative group comprising the six sixth roots of unity (as a subgroup of the multiplicative group of nonzero complex numbers)
 * The group of orientation-preserving symmetries (rotational symmetries) of the regular hexagon.