Results 1 to 2 of 2

Thread: Cosets

  1. #1
    Member
    Joined
    Aug 2008
    Posts
    97

    Cosets

    Let
    S be a subgroup of the group G. Suppose that a, b belongs to G

    satisfies
    Sa = bS. Thus the left coset of S containing a equals the right coset

    of
    S containing b. Show that Sa = aS = bS = Sb.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    May 2008
    Posts
    2,295
    Thanks
    7
    Quote Originally Posted by peteryellow View Post

    Let S be a subgroup of the group G. Suppose that a, b belongs to G satisfies Sa = bS. Thus the right coset of S containing a equals the left coset of S containing b.

    Show that Sa = aS = bS = Sb.
    from $\displaystyle Sa=bS,$ we get $\displaystyle a=bs,$ and $\displaystyle b=ta$ for some $\displaystyle s, t \in S.$ thus: $\displaystyle aS=bsS=bS=Sa=Sta=Sb.$
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Cosets
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: Nov 6th 2010, 04:26 PM
  2. cosets
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: Oct 27th 2009, 03:51 PM
  3. Cosets
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: Sep 22nd 2009, 02:40 PM
  4. Cosets
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: Dec 9th 2008, 03:22 PM
  5. cosets
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: Oct 7th 2008, 11:23 PM

Search Tags


/mathhelpforum @mathhelpforum