Results 1 to 2 of 2
Like Tree1Thanks
  • 1 Post By HallsofIvy

Math Help - Help with groups/homorphism?

  1. #1
    Newbie
    Joined
    Nov 2013
    From
    United Kingdom
    Posts
    1

    Help with groups/homorphism?

    Hi I'm doing some exercises on homorphisms and the first question is:

    Show
    p:C^*--->R, p(z)=log|z| (z is in C)
    is a homorphism.

    I know the method p(ab)=p(a)p(b) but how can I tell from this question which binary operations the groups use to prove it? I get this problem in other areas aswell. I thought maybe the * meant multiplicative and no * meant addition but in my notes it says the * means C\0.
    Thanks for any help.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,541
    Thanks
    1394

    Re: Help with groups/homorphism?

    Your first thought, that the "*" superscript indicates the operation is multiplication, is correct. What your book is saying is NOT that the "*" does not indicate multiplication. It is saying that the "C" does not indicate the entire complex numbers but the complex numbers without 0. That is necessary because the operation is multiplication and 0 does not have a multiplicative inverse.
    Last edited by HallsofIvy; November 21st 2013 at 08:53 AM.
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 8
    Last Post: March 30th 2012, 04:53 PM
  2. About minimal normal groups and subnormal groups
    Posted in the Advanced Algebra Forum
    Replies: 9
    Last Post: October 20th 2011, 01:53 PM
  3. Quotient Groups - Infinite Groups, finite orders
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: August 11th 2010, 07:07 AM
  4. Order of groups involving conjugates and abelian groups
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: February 5th 2009, 08:55 PM
  5. Homorphism Problem
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 27th 2007, 07:05 PM

Search Tags


/mathhelpforum @mathhelpforum