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.

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theperthvan	Just quickly, what is a generator in a group? 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 Recognitions: Homework Help Science Advisor	g generates G if G= <g^r : r in Z>, i.e. it is the cyclic group generated by g.

HallsofIvy Recognitions: Gold Member Science Advisor Staff Emeritus	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.