Results 1 to 2 of 2

Math Help - 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 Sa=bS, we get a=bs, and b=ta for some s, t \in S. thus: 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: November 6th 2010, 05:26 PM
  2. cosets
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: October 27th 2009, 04:51 PM
  3. Cosets
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: September 22nd 2009, 03:40 PM
  4. Cosets
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: December 9th 2008, 04:22 PM
  5. cosets
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: October 8th 2008, 12:23 AM

Search Tags


/mathhelpforum @mathhelpforum