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