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Belian group A that is the direct sum of cyclic groups

  1. May 11, 2004 #1
    If I have an abelian group A that is the direct sum of cyclic groups, say
    A=[tex]C_5 \oplus C_35[\tex], would I be right in saying the annihilator of A (viewed as a Z-module) is generated by (5,35)? If not, how do I find it?
     
  2. jcsd
  3. May 12, 2004 #2

    matt grime

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    ought it not to be an element of Z, which we presume is acting diagonally, and which is thus 35?
     
  4. May 12, 2004 #3
    I understand now, thanks. Now I also understand why you'd put the group into a form where each subscript divides the following, instead of just leaving it in primary form. It makes it much easier to find the annihilator.
     
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