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!

Showing this is surjective

  1. Nov 21, 2011 #1
    I have a mapping A_g:G ---> G defined by
    A_g(x) = g^-1(x)g (for all x in G)

    and as part of showing it is an automorphism i need show it is surjective.

    I'm not entirely sure how to do this but have made an attempt and would appreciate and feedback or hints to what I actually need to show. I know the definition of surjectivity and also that a mapping is surjective iff Im(of mapping) = G

    My attempt:
    It is surjective since if x is in G, then gxg^-1 is in G and then A_g(gxg^-1) = (g^-1)gx(g^-1)g = idxid = x.

    Thanks in advance
  2. jcsd
  3. Nov 22, 2011 #2


    User Avatar
    Science Advisor
    Homework Helper

    Yep, surjective just means that every element has a pre-image, and you have shown that by writing down the pre-image explicitly.
  4. Nov 22, 2011 #3
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Similar Threads for Showing surjective
I Showing that -a = (-1)*a