Just quickly, what is a generator in a group?

  1. 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,
     
  2. jcsd
  3. matt grime

    matt grime 9,396
    Science Advisor
    Homework Helper

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

    HallsofIvy 40,241
    Staff Emeritus
    Science Advisor

    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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