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!

Abstract Algebra.

  1. Feb 6, 2007 #1
    Please I need your help for that qustion and how do slove that qustion's problem. can you help me for slove for that? Pleasee

    Let G be any group, and let a, b ∈ G. Show that there are c, d ∈ G such that ac = b and da = b. Hint: you have to give an explicit definition for c and d in terms of a and b.
     
  2. jcsd
  3. Feb 6, 2007 #2

    mathwonk

    User Avatar
    Science Advisor
    Homework Helper

    what have you tried?
     
  4. Feb 6, 2007 #3
    I have tried set up matrices for that but not work. I don't know how to slove for this problem...


    Let G be any group, and let a, b ∈ G. Show that there are c, d ∈ G such that ac = b and da = b. Hint: you have to give an explicit definition for c and d in terms of a and b.
     
  5. Feb 6, 2007 #4

    morphism

    User Avatar
    Science Advisor
    Homework Helper

    Matrices?? All you need is:
    (i) if x is in G, then so is its inverse
    (ii) if x,y are in G, then so is xy
     
  6. Feb 6, 2007 #5
    i m tried work on this..

    GIVE a, b ∈ G
    SHOW c, d ∈ G ???

    ac=b da=b

    ac=b ---> proof: a (a^(-1)b)=b (IS THAT RIGHT? I THINK SO AND THAT'S RIGHT)

    da=b ---> proof: ???
     
  7. Feb 6, 2007 #6
    if i want to say about ac=b

    proof: a (a^(-1)b)=b
    uniqueness
    if ac=ad=b
    then c=d (left Cancellation)

    How do I slove for da=b?? I need for that..
     
  8. Feb 6, 2007 #7

    morphism

    User Avatar
    Science Advisor
    Homework Helper

    Same idea: let d = ba^(-1).
     
  9. Feb 8, 2007 #8
    Same idea: let d = ba^(-1). ?? I seem that not enough

    ac=b
    a (a^(-1)b)=b, if ac=ad=b, then c=d (left cancellation).. I m sure that's right.



    da=b
    d=ba(a^(-1)), if ad=ac=b, then d=c (right cancellation) is that right?????
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Abstract Algebra.
  1. Abstract Algebra (Replies: 1)

  2. Abstract Algebra (Replies: 5)

  3. Abstract Algebra (Replies: 6)

  4. Abstract Algebra (Replies: 0)

  5. Abstract Algebra (Replies: 9)

Loading...