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: Group Theory

  1. Apr 8, 2009 #1
    Suppose g[tex]\in[/tex] Isom C, z[tex]\in[/tex] C:

    Prove that the g-orbit of z is invariant under g.

    I just need some clarification on what this is asking for:

    1.) Are we assuming that g is a group of the isometries of C under composition?
    2.) To show invariance, would I only have to show that the g-orbit of z [tex]\in[/tex] C?


    Here's my guess at the proof:

    The g-orbit of z is defined as Orbitg(x) = {h(x)|h[tex]\in[/tex] g}, x[tex]\in[/tex] C.
    Now, for all h[tex]\in[/tex] g, h(z)[tex]\in[/tex] C since h[tex]\in[/tex] Isom C, which means h is an isometry from the complex plane to itself. QED.

    Thanks in advance.
     
  2. jcsd
  3. Apr 8, 2009 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    What does it mean for h to be an element of g if g is an element of Isom(C)? g isn't a set, is it? Can you clarify your definitions?
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...
Similar Threads for Group Theory
Are these homomorphisms?