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: Abstract Algebra: Commutative Subgroup

  1. Dec 16, 2009 #1
    1. The problem statement, all variables and given/known data

    Let G be a group and let a, b be two fixed elements which commute with each other (ab = ba). Let H = {x in G | axb = bxa}. Prove that H is a subgroup of G.

    2. Relevant equations


    3. The attempt at a solution

    I'm using the subgroup test. I know how to show that the identity of G exists in H and that if x1, x2 exist in H then x1 times x2 exists in H but need help proving that if x is in H then x^-1 is also in H. I've tried starting with axb = bxa and multiplying on the right and left with various combinations of a, x^-1, and b, but can't get it to the form ax^-1b = bx^-1a.

    Please let me know if you have any ideas, thanks.
  2. jcsd
  3. Dec 16, 2009 #2
    Prove that [b-1,a] = [b,a-1] = 0 and use that along with the fact that axb = bxa.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook