Results 1 to 4 of 4

Math Help - Does the group U(12) of units in Z/12 have the same structure as U(8)?

  1. #1
    Junior Member
    Joined
    Jan 2010
    Posts
    50

    Does the group U(12) of units in Z/12 have the same structure as U(8)?

    Does the group U(12) of units in Z/12 have the same structure as U(8)?

    I don't quite understand the question.
    Could you please explain what it means by "units" and by "structure"?
    Last edited by mr fantastic; May 6th 2010 at 06:54 PM. Reason: Copied title into main body of post.
    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 feyomi View Post
    I don't quite understand the question.
    Could you please explain what it means by "units" and by "structure"?
    A group of units is the group of elements another group that have an inverse.

    So in  \mathbb{Z}/12\mathbb{Z} , the group of units, or how you denote it  U(12) = \{1,5,7,11\} .
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jan 2010
    Posts
    50
    Quote Originally Posted by chiph588@ View Post
    A group of units is the group of elements another group that have an inverse.

    So in  \mathbb{Z}/12\mathbb{Z} , the group of units, or how you denote it  U(12) = \{1,5,7,11\} .


    How would I go about determining whether there is a correspondence between the two groups at hand?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by feyomi View Post
    How would I go about determining whether there is a correspondence between the two groups at hand?
    Do, what's obvious. Since \varphi(12)=\varphi(8)=4 draw out the two Cayley tables (not really but you get the idea) and figure out the isomorphism.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. What is a group structure?
    Posted in the Advanced Algebra Forum
    Replies: 7
    Last Post: June 16th 2011, 01:17 AM
  2. Group of units
    Posted in the Advanced Algebra Forum
    Replies: 7
    Last Post: November 1st 2010, 02:05 AM
  3. Group of Units
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: May 16th 2009, 01:47 PM
  4. group structure?
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: August 3rd 2008, 10:08 AM
  5. Group Structure
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 4th 2006, 03:13 PM

Search Tags


/mathhelpforum @mathhelpforum