1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Permutation Group Proof

  1. Oct 24, 2011 #1
    1. The problem statement, all variables and given/known data
    Suppose G is a group, H < G (H is a subgroup of G), and a is in G.

    Prove that a is in H iff <a> is a subset of H.


    2. Relevant equations
    <a> is the set generated by a (a,aa,aa^-1,etc)


    3. The attempt at a solution
    For some reason this seems too easy:

    1. Suppose a is in H.
    Since H is a group, a^-1 is in H.
    Since H is a group aa, is in H (as is aa^-1, etc.)
    Thus <a> is a subset of H.

    2. Suppose <a> is a subset of H.
    Obviously a is in H.

    And this completes the proof... or am I missing something?
     
  2. jcsd
  3. Oct 25, 2011 #2
    shameful bump
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook