Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    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.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook