A cyclic group is a group all of whose elements are powers of a particular element a . In multiplicative notation, the elements of the group are … … , a − − 3 , a − − 2 , a − − 1 , a 0 , a , a 2 , a 3 , … … , where a 2 means ⁠ a ⋅ ⋅ a ⁠, a − − 3 stands for ⁠ a − − 1 ⋅ ⋅ a − − 1 ⋅ ⋅ a − − 1 = ( a ⋅ ⋅ a ⋅ ⋅ a ) − − 1 ⁠, etc. Such an element a is called a generator or a primitive element of the group. In additive notation, the requirement for an element to be primitive is that each element of the group can be written as … … , ( − − a ) + ( − − a ) , − − a , 0 , a , a + a , … … .