We say the group of integers under addition Z has only two generators, namely 1 and -1.
However, Z can also be generated by any set of 'relatively prime' integers. (Integers having gcd 1).
I have two questions here. Couldn't find a satisfactory answer anywhere.
If a group is generated by a set consisting of a single element, only then is it cyclic?
Does 'generator' mean a single generating element?
Is it correct to say '(Z, +) has two generators but infinitely many generating sets'?
Thank you for your help!