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Primary Decomposition.

  1. Jan 18, 2013 #1
    1. The problem statement, all variables and given/known data

    Fourth example in this link: http://www.millersville.edu/~bikenaga/courses/345/reviews/revs2.pdf [Broken]

    2. Relevant equations



    3. The attempt at a solution

    I'm a bit confused, because...

    For the primary factor decomposition:
    Our textbook says...If G is any abelian group, then its p-primary component is [tex]G_p = \{ a\in G: p^na=0 \text{for some} n \geq 1\}[/tex].

    Every finite abelian group $G$ is the direct sum of its p-primary components:

    [tex]G = G_{p_1} \bigoplus ... \bigoplus G_{p_n}[/tex]

    For this example, we know that the primes are 2, 3, and 5.

    So isn't the primary decomposition supposed to be

    [tex]G = G_2 \bigoplus G_3 \bigoplus G_5[/tex]?

    Why is the answer in the link different?

    Thanks in advance
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
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