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Cosets math problem

  1. Jan 13, 2008 #1
    1. The problem statement, all variables and given/known data
    Let H be a subgroup of a finite group G. I understand that the cosets of H partition G into equivalence classes. Is it always true that each of these equivalence classes is a group?

    EDIT: clearly is it not always true; let H ={0,4,8,12} in Z_16 and take the right coset with 1; so are there conditions that make it true?
    2. Relevant equations

    3. The attempt at a solution
    Last edited: Jan 13, 2008
  2. jcsd
  3. Jan 13, 2008 #2
    I think the cosets form a group iff the subgroup H is normal.

    Edit: sorry I think I misread; are you asking if each coset forms a group or if the collection of cosets forms a group?
    Last edited: Jan 13, 2008
  4. Jan 13, 2008 #3


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    Only one coset can be a group. The one containing e. The quotient group (collection of cosets) can be a group as Mathdope alluded to.
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