Results 1 to 2 of 2

Math Help - Another problem in homomorphism and factor groups.....

  1. #1
    ynj
    ynj is offline
    Senior Member
    Joined
    Jul 2009
    Posts
    254

    Another problem in homomorphism and factor groups.....

    if H is the only subgroup of G that has order k(G may have many subgroups..),prove that H is normal in G....
    Thank you!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member PaulRS's Avatar
    Joined
    Oct 2007
    Posts
    571
    By definition: H is normal in G if and only if, for all g\in G we have gHg^{-1}=H

    Now, show that, for any g\in G , gHg^{-1} is in fact a subgroup of G that has order <br />
\left| {gHg^{ - 1} } \right| = \left| H \right|<br />
. Then the rest will follow since H is the only subgroup of that order in G.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Homomorphism and order of groups
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: October 15th 2011, 11:48 PM
  2. A tough problem in factor groups and homomophism
    Posted in the Advanced Algebra Forum
    Replies: 19
    Last Post: July 31st 2009, 07:00 AM
  3. Kernels and homomorphism of groups
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: April 20th 2009, 09:29 PM
  4. Homomorphism of Groups and their generators
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: December 1st 2008, 01:15 PM
  5. Replies: 0
    Last Post: May 1st 2008, 03:11 PM

Search Tags


/mathhelpforum @mathhelpforum