Results 1 to 4 of 4

Math Help - abstract algebra

  1. #1
    Member
    Joined
    Sep 2008
    Posts
    166

    abstract algebra

    Prove that if A is a subset of B, then <A> is a subgroup of <B>. Give an example where A is a subest of B with A =/= B but <A> = <B>.

    Please help.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by dori1123 View Post
    Prove that if A is a subset of B, then <A> is a subgroup of <B>. Give an example where A is a subest of B with A =/= B but <A> = <B>.
    \left< A \right> = \bigcap_{A\subseteq H} H - the intersection of all subgroups of the group containing A.
    \left< B \right> = \bigcap_{B\subseteq H} H - the intersection of all subgroups of the group containing B.

    Now since A\subseteq B it follows,
    \left< A \right> = \bigcap_{A\subseteq H}H \subseteq \bigcap_{B\subseteq H} H = \left< B \right>.

    For the example, let G = \mathbb{Z}_2 then \left< \{ [1] \} \right> = \left< G \right>.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Sep 2008
    Posts
    166
    Quote Originally Posted by ThePerfectHacker View Post
    For the example, let G = \mathbb{Z}_2 then \left< \{ [1] \} \right> = \left< G \right>.
    Is \mathbb{Z}_2 the same as Z/2Z?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by dori1123 View Post
    Is \mathbb{Z}_2 the same as Z/2Z?
    Yes
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: December 6th 2010, 04:03 PM
  2. Replies: 0
    Last Post: April 24th 2010, 12:37 AM
  3. Abstract Algebra
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: October 22nd 2008, 06:21 PM
  4. Abstract Algebra
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: October 16th 2008, 08:26 AM
  5. Abstract Algebra help
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: April 12th 2008, 02:59 AM

Search Tags


/mathhelpforum @mathhelpforum