Question on non abelian group of order 6

[Kurchi]

Why any non abelian group of order 6 has no element of order 6?

 

[Deleted member 4993]

Why any non abelian group of order 6 has no element of order 6?

Please show us what you have tried and exactly where you are stuck.

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[HallsofIvy]

First, what does "element of order 6" mean? Suppose there were an "element of order 6". What can you say about its inverse?

 

[pka]

Why any non abelian group of order 6 has no element of order 6?

What can we say about a subgroup \(<a>\) generated by an element of the group?

 

[Steven G]

Do you know what a cyclic group is? Can a cyclic group be non abelian?