- #1

Daveyboy

- 58

- 0

## Homework Statement

Prove any cyclic group with more than two elements has at least two different generators.

## Homework Equations

A group G is cyclic if there exists a g in G s.t. <g> = G. i.e all elements of G can be written in the form g^n for some n in Z.

## The Attempt at a Solution

Z has 1 and -1.

<i> where i = (-1)^1/2 so i and -i work

now I consider G={e, a, a^2}

All I can think of is a^3 could generate this aside from a, but that is pretty lame. Am I missing somethig?