1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework: find right coset of a group

  1. Aug 12, 2010 #1
    1. The problem statement, all variables and given/known data

    Let G be a group, H is subgroup of G, and [G:H]=2
    find all the right and left coset of H in G

    2. Relevant equations

    n/a

    3. The attempt at a solution

    (finding right coset)

    so there exist 2 distinct right coset, but how to find the 2 right coset?

    let a,b in G

    so Ha and Hb are the right coset if Ha[tex]\cap[/tex]Hb={}

    then?
     
  2. jcsd
  3. Aug 12, 2010 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Re: Coset

    Pick an a in G that is not in H. Then the right cosets are H and Ha, right?
     
  4. Aug 12, 2010 #3
    Re: Coset

    yes, and is that the answer?

    let a in G not in H

    H and Ha are the right coset of H in G
    H and aH are the left coset of H in G
    is that correct and sufficient?

    what if i do like this

    let ab-1 in G not in H

    Ha and Hb are the right coset of H in G
    aH and bH are the left coset of H in G
    it's the same thing right?
     
  5. Aug 12, 2010 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Re: Coset

    Same thing, yes. But I don't know that it really helps you in any way. I think the point is that there is only one right coset that is not equal to H and there is only one left coset that is is not equal to H. So they must be equal. Isn't that the point?
     
  6. Aug 12, 2010 #5
    Re: Coset

    yea, haha, like you said, i wanted to show Hx=xH for all x in G, thank you very much,
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Homework: find right coset of a group
  1. Right Cosets (Replies: 5)

Loading...