Results 1 to 2 of 2

Math Help - permutation/transitivity

  1. #1
    Junior Member
    Joined
    Oct 2009
    Posts
    56

    permutation/transitivity

    Prove: Let H be a finite group of permutations of the set Y. Suppose Y acts transitivity on Y. Then Y is a finite set, and |Y|divide |H|
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Apr 2009
    From
    México
    Posts
    721
    It's a standard theorem that H/St_H(x) \equiv orb(x) as H-sets where St_H(x):= \{ h \in H : hx=x \} and orb(x)= \{ hx \in Y : h\in H \} and since H acts transitively orb(x)=Y so we have \vert H \vert = \vert orb(x) \vert \vert St_H(x) \vert = \vert Y \vert \vert St_H(x) \vert and the result is immediate.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Need help with proving transitivity property
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: April 9th 2010, 08:13 AM
  2. Transitivity
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: October 12th 2009, 09:13 PM
  3. mod proof by induction uses transitivity
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: May 3rd 2009, 12:19 PM
  4. [SOLVED] Transitivity in set relations
    Posted in the Discrete Math Forum
    Replies: 11
    Last Post: October 11th 2008, 05:48 PM
  5. reflexive, transitivity
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: September 4th 2008, 07:35 PM

/mathhelpforum @mathhelpforum