Results 1 to 2 of 2

Math Help - finitely generated groups

  1. #1
    mms
    mms is offline
    Junior Member
    Joined
    Jul 2009
    Posts
    67

    finitely generated groups

    Show that if H is a normal subgroup of a group G such that H and G/H are finitely generated, then so is G

    thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    May 2008
    Posts
    2,295
    Thanks
    7
    Quote Originally Posted by mms View Post
    Show that if H is a normal subgroup of a group G such that H and G/H are finitely generated, then so is G

    thanks!
    let H=<h_1, \cdots , h_m>, \ G/H = <Hg_1, \cdots , Hg_n>, and g \in G. then g \in H<g_1, \cdots , g_n> \subseteq <h_1, \cdots ,h_m,g_1, \cdots , g_n>. thus: G \subseteq <h_1, \cdots , h_m, g_1, \cdots , g_n> \subseteq G.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finitely Generated Abelian Groups
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: March 4th 2012, 06:32 AM
  2. intersection of finitely generated groups
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: June 23rd 2010, 01:34 AM
  3. free groups, finitely generated groups
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: May 23rd 2009, 04:31 AM
  4. finitely generated Abelian groups
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: April 19th 2009, 03:34 AM
  5. Replies: 5
    Last Post: January 22nd 2007, 08:51 PM

Search Tags


/mathhelpforum @mathhelpforum