Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor
    Homework Helper

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook