# Belian group A that is the direct sum of cyclic groups

1. May 11, 2004

### Nexus[Free-DC]

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. May 12, 2004

### matt grime

ought it not to be an element of Z, which we presume is acting diagonally, and which is thus 35?

3. May 12, 2004

### Nexus[Free-DC]

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.