Results 1 to 2 of 2

Math Help - Calculating Rank and Torsion Coefficients

  1. #1
    Member
    Joined
    Jun 2007
    Posts
    131

    Calculating Rank and Torsion Coefficients

    How do i calculate the rank and torsion coefficients of the following:

    B=Z3 x Z14 x Z24 x Z126 x Z
    C = <a,b,c,d: 168b=0, 42c=0, 18d=0>

    Am i right in thinking that B can be decomposed to:

    Z3=Z3
    Z14=Z2 x Z7
    Z24 = Z3 x Z8
    Z126 = Z2 x Z9 x Z7

    Of so how, do I combine to get the torsion and rank coefficient?

    Also, for C, am I right in thinking that this is Z0 x Z168 x Z42 x Z18

    If, so can someone help me decompose this and recombine so i can calculate rank and torsion
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by moolimanj View Post
    How do i calculate the rank and torsion coefficients of the following:

    B=Z3 x Z14 x Z24 x Z126 x Z
    C = <a,b,c,d: 168b=0, 42c=0, 18d=0>

    Am i right in thinking that B can be decomposed to:

    Z3=Z3
    Z14=Z2 x Z7
    Z24 = Z3 x Z8
    Z126 = Z2 x Z9 x Z7

    Of so how, do I combine to get the torsion and rank coefficient?
    If you have the group G=\mathbb{Z}_{q_1}\times ... \times \mathbb{Z}_{q_k} \times \mathbb{Z}^n then the torsion subgroup is \mathbb{Z}_{q_1}\times ... \times \mathbb{Z}_{q_k}. Where the q_i str prime powers, not necessarily distinct. If we form the torsion subgroup T\times \{ 0\}^n and we mod it out, i.e. compute G/T \simeq \mathbb{Z}^n. Thus, G/T is a free abelian group. The "rank" is the # of elements in a basis for G. Since all basis has the same number of elements we see that \{ (1,0,...,0),(0,1,...,0),...(0,0,...,1)\}. And so the rank is n.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Calculating coefficients
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 4th 2011, 01:55 PM
  2. Calculating the Rank Correlation Coefficient
    Posted in the Statistics Forum
    Replies: 0
    Last Post: March 9th 2011, 07:54 AM
  3. Replies: 0
    Last Post: November 5th 2010, 08:08 AM
  4. Average rank correlation coefficients
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: April 12th 2010, 03:41 AM
  5. Torsion coefficients
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 15th 2009, 04:28 PM

Search Tags


/mathhelpforum @mathhelpforum