Results 1 to 3 of 3

Math Help - Normal Subgroups of A Group

  1. #1
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9

    Normal Subgroups of A Group

    1)If a group is abelian then all its subgroups are normal.
    But turn the question around,
    If all the subgroups of a group are normal then it is abelian?

    I was not able to show that.
    Since this is my own question I believe that is is wrong.

    I think we should consider cases when the group is finite and infinite. Maybe that will help because if it is finite then it has a composition series (but I am not sure what that leads to).
    Last edited by ThePerfectHacker; January 20th 2007 at 02:55 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by ThePerfectHacker View Post
    1)If a group is abelian then all its subgroups are normal.
    But turn the question around,
    If all the subgroups of a group are normal then it is abelian?
    No; see here.

    RonL
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    That is not exactly what I was looking for (I was hoping y conjecture to be true). But thank you.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Subgroups and Intersection of Normal Subgroups
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: December 1st 2010, 08:12 PM
  2. subgroups and normal subgroups
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 19th 2010, 03:30 PM
  3. Replies: 1
    Last Post: March 18th 2010, 02:15 AM
  4. Normal subgroups of a group
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 8th 2009, 01:33 PM
  5. Subgroups and normal subgroups
    Posted in the Advanced Algebra Forum
    Replies: 8
    Last Post: October 13th 2007, 04:35 PM

Search Tags


/mathhelpforum @mathhelpforum