1. Limited time only! Sign up for a free 30min personal 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!

Coset Question

  1. Feb 12, 2012 #1
    Let H and K be Subgroups
    show Ha[itex]\cap[/itex]Ka = (H[itex]\cap[/itex]K)a for all a [itex]\in[/itex]G

    pf

    Let x[itex]\in[/itex]Ha[itex]\cap[/itex]Ka

    Then x[itex]\in[/itex]Ha and x[itex]\in[/itex]Ka

    Can I just say that x [itex]\in[/itex](H[itex]\cap[/itex]K)a ? Or am I missing something.
     
  2. jcsd
  3. Feb 12, 2012 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    hi Punkyc7! :smile:
    nooo :redface:

    your next word should be "∃" :wink:
     
  4. Feb 12, 2012 #3
    huh?
     
  5. Feb 12, 2012 #4

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    sorry, that character doesn't show up on some computers :redface:

    your next words should be "there exists a y such that …" :smile:
     
  6. Feb 12, 2012 #5
    Ok so there exist a y such that y is in Ha and Ka. Then is it right?
     
  7. Feb 12, 2012 #6

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    no!!

    x is in Ha and Ka, so there exists a y in … such that … ? :smile:
     
  8. Feb 12, 2012 #7
    bear with me..

    There exist a y in (H[itex]\cap[/itex]K)a such that x=ya?
     
  9. Feb 12, 2012 #8

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    not quite

    read it and try again :smile:
     
  10. Feb 12, 2012 #9
    is it a y in G? such that x=ya? Then im not sure if I need the a anymore.
     
  11. Feb 12, 2012 #10

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    no!

    once again :smile:
     
  12. Feb 12, 2012 #11
    ok Im sure where the y is floating around but if its not in G or (H[itex]\cap[/itex]k)a. The only place left would have to be just H[itex]\cap[/itex]K right
     
  13. Feb 12, 2012 #12

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    yes!!!!! :smile:

    now, can you see why?
     
  14. Feb 12, 2012 #13

    Deveno

    User Avatar
    Science Advisor

    suppose y is in both Ha and Ka.

    what does this mean?

    it means y = ha, for some h in H, and y = ka, for some k in K.

    for this h, and this k:

    ha = ka.

    can you think of something to do with this? (perhaps multiply both sides by something?)

    *****

    that is only HALF the problem, though. the other half means you suppose:

    y is in (H∩K)a.

    what can you do with this?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Coset Question
  1. Cosets of Subgroups (Replies: 1)

  2. Right Cosets (Replies: 5)

  3. Question about Cosets (Replies: 2)

Loading...