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: Stabiliser Groups of a vertex/edge of a square

  1. Sep 27, 2012 #1
    1. The problem statement, all variables and given/known data

    Given the dihedral group of symmetries of a square; what is the stabiliser group of a vertex (or edge)?

    2. Relevant equations
    The stabiliser group is G_x={g[itex]\in[/itex]G|gx=x}
    I guess for a vertex/edge that means the transformations in D4 (generated by reflection in x axis and rotation by 90°)

    3. The attempt at a solution
    Doodling in my notebook, I have determined that the only way that the order of vertices/edges can be changed is by reversing them - which means that the only unique elements of G that map a vertex/edge to itself is the identity, and one other - which depends on the vertex/edge, but is basically a rotation combined with a reflection, that reverses the order of the vertices and then rotates it back to the relevant spot... are theere any others? and how can I do it algebraically to demonstrate a complete stabilising subgroup?
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted