Re: Quotient group question

On Mon, 4 Feb 2008, quasi wrote:
<marsh@xxxxxxxxxxxxxxxxxx> wrote:

On Mon, 4 Feb 2008, [ISO-8859-1] José Carlos Santos wrote:
On 04-02-2008 10:24, *** wrote:

Here's another question: what is the smallest normal subgroup H of Z*Z
such that (Z*Z)/H is isomorphic to Z?

What about answering first to the questions raised by your previous
question?

He tacidly addressed them with his revised question.
There is however, no smallest normal subgroup of Z^2.

The group in question is Z*Z, not Z^2.

There's a difference?

The smallest normal subgroup of every group is the trivial group.

There is no smallest non-trivial normal subgroup of ZxZ. The all of them
have the same size. Even if ordered by set inclusion, there is still no
smallest non-trival subgroup of Z+Z.

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