Results 1 to 2 of 2

Math Help - Group Axioms Help

  1. #1
    Member
    Joined
    Jun 2007
    Posts
    131

    Group Axioms Help

    Hi all

    If G is a group with identity e and if A and B and subgroups of G then A*B is a subgroup of G*G.

    How do I use this to show that if A and B are two normal subgroups of G, then A*B is a normal subgroup of G*G?

    Also, if H is the subset H={(g,g):gEG} how do i show that H is a subgroup of G*G?

    Thanks again - and sorry for the previous posts around groups and geometry (not my strongest subjects)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by moolimanj View Post
    Hi all

    If G is a group with identity e and if A and B and subgroups of G then A*B is a subgroup of G*G.
    GG=G thus AB being a subgroup of GG means AB is subgroup of G. But that is not true. If one of A,B is normal then it is true. In general it is not.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Group Axioms G4 Associative
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: March 23rd 2011, 06:10 AM
  2. Group Axioms
    Posted in the Advanced Algebra Forum
    Replies: 7
    Last Post: March 9th 2011, 06:15 AM
  3. Axioms
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: September 10th 2009, 11:28 AM
  4. Inner Product Axioms
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: April 27th 2009, 04:48 AM
  5. Axioms Proving.
    Posted in the Statistics Forum
    Replies: 1
    Last Post: March 15th 2009, 12:41 AM

Search Tags


/mathhelpforum @mathhelpforum