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2 Answers

5 votes
5 votes
G is not group here...

For eg 3*2 mod 6=0

0 is not in G

 G is not satisfying closure property..so it is not group
1 votes
1 votes

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 afor 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 

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. 

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