Results 1 to 3 of 3

Thread: Generator

  1. October 21st 2009, 09:54 AM #1
    GTK X Hunter
    GTK X Hunter is offline
    Junior Member
    Joined
    Oct 2009
    Posts
    44

    Generator

    Let p be a prime number. Then how many generators of the cyclic group Z_{p^r}, with r\in\mathbb{Z} and r\ge 1
    Follow Math Help Forum on Facebook and Google+
  2. October 21st 2009, 11:58 AM #2
    tonio
    tonio is offline
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Quote Originally Posted by GTK X Hunter View Post
    Let p be a prime number. Then how many generators of the cyclic group Z_{p^r}, with r\in\mathbb{Z} and r\ge 1

    \mbox{An element}\,\,x\in Z_{p^r}\,\,\mbox{is a generator iff}\,\,(x,p^r)=1\,\,\mbox{, so there are....generators}

    Tonio
    Follow Math Help Forum on Facebook and Google+
  3. March 27th 2010, 12:41 AM #3
    GTK X Hunter
    GTK X Hunter is offline
    Junior Member
    Joined
    Oct 2009
    Posts
    44
    Quote Originally Posted by tonio View Post
    \mbox{An element}\,\,x\in Z_{p^r}\,\,\mbox{is a generator iff}\,\,(x,p^r)=1\,\,\mbox{, so there are....generators}

    Tonio
    you mean the gcd (x,p^r)=1?
    Follow Math Help Forum on Facebook and Google+
« Generator of group | Linear operator proof »

Similar Math Help Forum Discussions

  1. Generator for an ideal
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: December 4th 2011, 06:30 AM
  2. generator for groups.
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: October 29th 2010, 12:10 AM
  3. generator of an ideal , I really need help
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: April 13th 2010, 02:02 AM
  4. Generator of group
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: March 27th 2010, 12:24 AM
  5. generator matrix
    Posted in the Advanced Algebra Forum
    Replies: 7
    Last Post: November 22nd 2008, 12:06 AM

Search Tags


/mathhelpforum @mathhelpforum