- #1
Daveyboy
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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?