Cyclic Group Of order = 12 with generator = a has elements {a,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12}
Order of generator = Order of group = 12
Order of an element is the smallest positive integer such that an is identity element.
Identity element = a12
Other Generators are = {a5,a7,a11}
Order of every subgroup divides the order of group.
Order of Subgroup |
SubGroup |
1 |
a12 |
2 |
a6,a12 |
3 |
a4,a8,a12 |
4 |
a3,a6,a9,a12 |
6 |
a2,a4,a6,a8,a10,a12 |