finite cyclic simple groups can be generated by two elements

66 Views Asked by At

With reference to Peter Clark answer here, I have the following question ( I think it is not difficult but I am not able to see how it can be done )

He says most finite simple groups can be generated by two elements $G=<x,y>$ where $x$ has order 2 and $y$ has order 3.

Suppose I take $G=\mathbb{Z}/p\mathbb{Z}$ where $p$ is a prime, I am not able to see how as every non trivial element has order $p$.

May be by "most finite simple groups " he mean non Abelian simple groups.Kindly correct me If I have made some mistake.

Edit :

I want to study this result,If somebody know the reference Kindly mention it. Thanks in advance.