Results 1 to 3 of 3

Math Help - Units in Z20

  1. #1
    Super Member
    Joined
    Feb 2008
    Posts
    535

    Units in Z20

    Make a list of units in Z20 and verify that they all map to units in Z4. Show that ther is a non-unit in Z20 that maps to a unit in Z4.

    Please help... No idea how to do this...

    Thanks in advance for any help
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor chiph588@'s Avatar
    Joined
    Sep 2008
    From
    Champaign, Illinois
    Posts
    1,163
    Quote Originally Posted by jzellt View Post
    Make a list of units in Z20 and verify that they all map to units in Z4. Show that ther is a non-unit in Z20 that maps to a unit in Z4.

    Please help... No idea how to do this...

    Thanks in advance for any help
     a\in\mathbb{Z}/20\mathbb{Z} is a unit  \iff (a,20)=1 .

    Therefore the group of units of  \mathbb{Z}/20\mathbb{Z} is  \left(\mathbb{Z}/20\mathbb{Z}\right)^\times = \{1,3,7,9,11,13,17,19\} .

     \left(\mathbb{Z}/4\mathbb{Z}\right)^\times = \{1,3\} .

    Now what kind of map are we talking about here? An isomorphism?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Feb 2008
    Posts
    535
    I'm not really sure what is meant by "map" either, but thanks for the reply. This will at least get me started...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Units
    Posted in the Number Theory Forum
    Replies: 0
    Last Post: February 11th 2010, 03:34 PM
  2. Units
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: April 21st 2009, 10:42 PM
  3. Replies: 3
    Last Post: November 15th 2008, 05:18 AM
  4. Units Mod N
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: March 9th 2008, 09:47 AM
  5. SI units Q
    Posted in the Advanced Applied Math Forum
    Replies: 1
    Last Post: October 1st 2007, 02:59 PM

Search Tags


/mathhelpforum @mathhelpforum