# Primary Decomposition.

1. Jan 18, 2013

### Artusartos

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 $$G_p = \{ a\in G: p^na=0 \text{for some} n \geq 1\}$$.

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

$$G = G_{p_1} \bigoplus ... \bigoplus G_{p_n}$$

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

So isn't the primary decomposition supposed to be

$$G = G_2 \bigoplus G_3 \bigoplus G_5$$?