If in a Group there is atleast one generator present then we can say Group is cyclic.
A Group(G,*) is called a cyclic group if there exist an element a∈G such that every element of G can be written as an for some integer n.Then a is called generating element or generator.
Before check Group is cyclic Group or not we have to check given set is Group or not.
Simply Make composition table for check it
| ⊗6 | 1 | 2 | 3 | 4 | 5 | 6 |
| 1 | 1 | 2 | 3 | 4 | 5 | 0 |
| 2 | 2 | 4 | 0 | 2 | 4 | 0 |
| 3 | 3 | 0 | 3 | 0 | 3 | 0 |
| 4 | 4 | 2 | 0 | 4 | 2 | 0 |
| 5 | 5 | 4 | 3 | 2 | 1 | 0 |
| 6 | 0 | 0 | 0 | 0 | 0 | 0 |
Here elements 2,3,4 and 6 doesn't have inverse that is necessary to make a Group.
Alternate way check Given set is Group or not:-
To make a Group following conditions should be satisfy:
1.Closure Property
2.Associativity
3.Identity
4.Inverse
By 1st property
1 ⊗6 6 = 0 but 0 is not present in set.
given set is not a Group.
Given set can't be cyclic Group so there is no Generator present.
