This may not be much of a problem but I have to give the whole diagram just in case. We have two homomorphic short exact sequences:

$\displaystyle 0 \to \mathbb{Z} \to \mathbb{Z} \to \mathbb{Z} / 2 \mathbb{Z} \to 0$

with functions: $\displaystyle n: \mathbb{Z} \to \mathbb{Z}$ and $\displaystyle \pi : \mathbb{Z} \to \mathbb{Z} / 2 \mathbb{Z}$

This is to be taken as a homomorphic map to the the other short exact sequence:

$\displaystyle 0 \to \mathbb{Z} / k \mathbb{Z} \to \mathbb{Z} / m \mathbb{Z} \to \mathbb{Z} / n \mathbb{Z} \to 0$

with functions $\displaystyle i: \mathbb{Z} / k \mathbb{Z} \to \mathbb{Z} / m \mathbb{Z}$ and $\displaystyle \pi ' : \mathbb{Z} / m \mathbb{Z} \to \mathbb{Z} / n \mathbb{Z}$

With homomorphisms "dropping from the first sequence to the second one" given by $\displaystyle \alpha : \mathbb{Z} \to \mathbb{Z} / k \mathbb{Z}$ and $\displaystyle \beta : \mathbb{Z} \to \mathbb{Z} / m \mathbb{Z}$ and $\displaystyle \gamma : \mathbb{Z} / n \mathbb{Z} \to \mathbb{Z} / n \mathbb{Z}$

Sorry for the ugly notations above. I'm linking a pdf with a similar diagram for at least a little more clarity. Does anyone know how to code the LaTeX for this diagram?

Okay, my question is about $\displaystyle n : \mathbb{Z} \to \mathbb{Z}$. What is this function? I would just call it a mapping but the letter n also shows up in $\displaystyle \mathbb{Z} / n \mathbb{Z}$ where n is an integer. Is this just poor notation on my text's part or am I missing something about the mapping n?

Thanks for any help.

In the pdf you are looking for equation (1.2) at the bottom of the first page. In my notation we have $\displaystyle \alpha , ~ \beta , ~\gamma$ in the diagram where the id, $\displaystyle \theta$, and id homomorphism are (respectively) in the diagram.

-Dan