1. Not finding help here? Sign up for a free 30min 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!

Homomorphism of groups

  1. Dec 12, 2013 #1
    1. The problem statement, all variables and given/known data
    Show that
    ##f(e)=e'## and ##f(g^-1)=f(g)^-1##



    2. Relevant equations
    Homomorphism
    f(x\cdot y)=f(x)\cdot f(y)



    3. The attempt at a solution
    I show the first one. Neutral element is element which satisfied
    ##e\cdot e=e##.
    So
    ##f(e)=f(e\cdot e=e)=f(e)\cdot f(e)##
    So ##f(e)=e'##.
    But how to show
    ##f(g^{-1})=f(g)^{-1}##?
     
  2. jcsd
  3. Dec 12, 2013 #2

    pasmith

    User Avatar
    Homework Helper

    What is [itex]f(gg^{-1})[/itex]?
     
  4. Dec 12, 2013 #3
    Tnx.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Homomorphism of groups
  1. Group homomorphism (Replies: 2)

  2. Group Homomorphism (Replies: 1)

  3. Group Homomorphism? (Replies: 3)

Loading...