I am just starting out with abstract algebra and am still getting my head around the first few concepts.
We have been asked to find out how many elements of the Z mod 6 quotient group are generators.
Does this mean that I look for the least amount of elements required to generate the Z mod 6 group?
or all of them.
I am not sure this is right but from my understanding the Z mod 6 group contains 6 equivalence classes with the [0] equivalence class being the identity.
If I took [1] I think its inverse would be [5] as that would give me back [0].
So would the generators be {[1],[2],[3]}?
As the inverses would give me [5] and [4] and the inverse of [3] would give me the identity?
Any clarification would be much appreciated, I think my confusion comes from not quite yet fully grasping the concepts.
Also if I am looking for ALL the genrators would {[3],[4],[5]} also work?