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Just quickly, what is a generator in a group?

by theperthvan
Tags: generator, quickly
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theperthvan
#1
Oct8-07, 01:29 AM
P: 184
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,
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matt grime
#2
Oct8-07, 03:33 AM
Sci Advisor
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P: 9,396
g generates G if G= <g^r : r in Z>, i.e. it is the cyclic group generated by g.
HallsofIvy
#3
Oct8-07, 06:52 AM
Math
Emeritus
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Thanks
PF Gold
P: 39,497
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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