Results 1 to 2 of 2

Math Help - normal

  1. #1
    Junior Member mathemanyak's Avatar
    Joined
    Jul 2008
    From
    TURKEY
    Posts
    39

    normal

    Let G be a group and H,K is a normal subgroup of G
    Prove that <HUK>=HK
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member JaneBennet's Avatar
    Joined
    Dec 2007
    Posts
    293
    x\in\left<H\cup K\right>\ \Rightarrow\ x=y^n for some y\in H\cup K,\ n\in\mathbb{Z}

    y\in H\ \Rightarrow\ x=y^n\cdot e\in HK
    y\in K\ \Rightarrow\ x=e\cdot y^n\in HK

    \therefore\ \left<H\cup K\right>\subseteq HK

    For the reverse inclusion, use the fact that H and K are normal in G.

    hk\in HK\ \Rightarrow\ hk=(hkh^{-1})h\in H and hk=k(k^{-1}hk)\in K

    \therefore\ HK\subseteq \left<H\cup K\right>
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: January 16th 2012, 07:21 PM
  2. A normal Moore space is completely normal
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: March 19th 2011, 12:52 PM
  3. Replies: 2
    Last Post: November 18th 2010, 08:22 AM
  4. Normal / Bivariate Normal distribution
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: May 24th 2010, 03:42 AM
  5. Replies: 1
    Last Post: April 20th 2008, 06:35 PM

Search Tags


/mathhelpforum @mathhelpforum