Question

Find the number of generators of a cyclic group having the given order 12

Answer 1

A cyclic group is a group that is generated by a single element. That means that there exists an element gg, say, such that every other element of the group can be written as a power of gg. This element gg is the generator of the group.





To obtain the generators of a cyclic group of order 12 consider the set of integers mod 12

{0 1 2 3 4 5 6 7 8 9 10 11}

Determine elements in the set that are relatively prime to 12. I mean get numbers from this set such that the gcd of the number and 12 is 1.

Such numbers are set to be generators of the group.