Re: Some group presentations

On 5 nov, 07:16, Derek Holt <ma...@xxxxxxxxxxxxx> wrote:
On 5 Nov, 04:00, "maxblac...@xxxxxxxxx" <maxblac...@xxxxxxxxx> wrote:

On 9 set, 02:31, berwald.f...@xxxxxxxxxxxxxx wrote:

Dear Jack,

Thanks once more for all your answers!
They were great.

Best,
Fred.

I have a silly question: what is the group presentation of the
cartesian product of groups (the support is not necessarly finite) -
not the direct product.

It makes no sense to talk about "the group presentation". Any group
has infinitely many presentations.

For any group G, you can always define the "regular" presentation,
which is essentially just the multiplication table of the group. That
is,  < X | R >, where X is the underlying set of G, and
R = { g h [gh]^-1 | g, h in G }, where [gh] denotes the product of g
and h in G.

For a Cartesian product, I don't know of any more "natural"
presentation.

Derek Holt.

< g (g in G)


Sorry, but I really meant the most natural one.
Thanks.
.

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