Just quickly, what is a generator in a group?

[theperthvan]

Just quickly, what is a generator in a group?
I have a question:
"Give an example of an element in (Z_28,⊕) which is not a generator."
Cheers,

 

[matt grime]

g generates G if G= <g^r : r in Z>, i.e. it is the cyclic group generated by g.

 

[HallsofIvy]

As far as "Give an example of an element in (Z_28,⊕) which is not a generator." is concerned, an obvious element that is never a generator is the group identity. If you want a less trivial example try any element that is a factor of 28.