Re: Hom(Z x Z, Z) - is it a cyclic group

From: "Mariano Suárez-Alvarez" <mariano.suarezalvarez@xxxxxxxxx>
Date: Tue, 22 Jan 2008 07:01:46 -0800 (PST)

On Jan 22, 12:06 pm, Christopher Kolago <precar...@xxxxxxxx> wrote:

Is a group of all homomorphisms from (Z x Z) to Z cyclic or is it not? As far as I can remember it's not cyclic (I solved this problem about a year ago, but today I'm somehow unable to prove it; bad day, I think...)

Take the two projection maps p_1, p_2 : Z x Z --> Z. It is
clearly false that either p_1 is a multiple of p_2 or
p_2 is a multiple of p_1.

-- m
.

References:
- Hom(Z x Z, Z) - is it a cyclic group
  - From: Christopher Kolago

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