Results 1 to 3 of 3

Math Help - normal subgroup...

  1. #1
    TTB
    TTB is offline
    Junior Member
    Joined
    Aug 2009
    Posts
    26

    normal subgroup...

    Let r be a subgroup of G.

    Let Ar be the set of all products (finite) of elements of the form (gi ri gi^-1) or (gi ri^-1 gi^-1) i = 1 to n.

    How can one show that Ar is normal in G.

    Thanks x
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Quote Originally Posted by TTB View Post
    Let r be a subgroup of G.

    Let Ar be the set of all products (finite) of elements of the form (gi ri gi^-1) or (gi ri^-1 gi^-1) i = 1 to n.

    How can one show that Ar is normal in G.

    Thanks x

    Isn't it clear this question belongs in "Abstract Algebra and Linear Algebra"??

    Anyway, this is trivial when one realizes that x^{-1}(ab)x=(x^{-1}ax)(x^{-1}bx). The set that you denoted Ar is more usually denoted by r^G and it's called
    the normal closure of the subgroup r in G.
    It also way more usual to denote sets, groups, subgroups, etc. with capital letters...

    Tonio
    Follow Math Help Forum on Facebook and Google+

  3. #3
    TTB
    TTB is offline
    Junior Member
    Joined
    Aug 2009
    Posts
    26
    Tonio - you are right, this should be in Abstract Algebra - my apologies, i must have typed it in the wrong forum by accident.

    I know that capital letters are the norm, I just wanted to make the notation clearer.

    Thanks x
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: March 2nd 2011, 08:07 PM
  2. Subgroup of cyclic normal subgroup is normal
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 25th 2010, 06:13 PM
  3. characterisitic subgroup implies normal subgroup
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: April 8th 2010, 03:13 PM
  4. subgroup of a normal subgroup...
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: November 23rd 2009, 08:06 AM
  5. Normal subgroup interset Sylow subgroup
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: May 10th 2008, 12:21 AM

Search Tags


/mathhelpforum @mathhelpforum