Results 1 to 2 of 2

Math Help - Cyclic Groups

  1. #1
    Junior Member hercules's Avatar
    Joined
    Sep 2007
    From
    Earth
    Posts
    62

    Cyclic Groups

    Please help me with this proof.

    Prove that if a group G has no subgroup other than G and {e}, then G is cyclic.

    Thanks.
    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 hercules View Post
    Please help me with this proof.

    Prove that if a group G has no subgroup other than G and {e}, then G is cyclic.

    Thanks.
    If G=\{ e\} then nothing to prove. Otherwise let a\in G, a\not = e, create the subgroup H=\left< a\right>, note H\not = \{ e\}. So, what does that means? And how does that complete the proof.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Automorphism groups of cyclic groups
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: August 15th 2011, 09:46 AM
  2. cyclic groups
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: February 25th 2010, 07:29 PM
  3. Cyclic Groups
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: November 3rd 2009, 07:26 AM
  4. Cyclic groups.
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: May 2nd 2009, 04:33 PM
  5. cyclic groups
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 17th 2008, 04:24 AM

Search Tags


/mathhelpforum @mathhelpforum