Given a set of generators for a group G, how do I find a presentation for it using those generators?

[Will]

Suppose I have a group G, which I know is finitely presentable and infinite.

Suppose I have a small list of generators for G (in this case, 5). How can I find a presentation for G using those generators?

thanks,

- will

[David Joyner]

On Fri, Apr 4, 2014 at 12:43 AM, Will <oxe...@gmail.com> wrote:
> Suppose I have a group G, which I know is finitely presentable and infinite.
>
> Suppose I have a small list of generators for G (in this case, 5). How can I find a presentation for G using those generators?
>

How do you define the group if you don't know what the presentation is?

> thanks,
>
> - will
>
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[Simon King]

Hi David,

On 2014-04-04, David Joyner <wdjo...@gmail.com> wrote:
> On Fri, Apr 4, 2014 at 12:43 AM, Will <oxe...@gmail.com> wrote:
>> Suppose I have a group G, which I know is finitely presentable and infinite.
>>
>> Suppose I have a small list of generators for G (in this case, 5). How can I find a presentation for G using those generators?
>>
>
> How do you define the group if you don't know what the presentation is?

Say, you got a matrix group and want a (minimal?) presentation by
generators and relations?

Best regards,
Simon

[Volker Braun]

I don't understand the question but the answer is most likely somewhere here: 

http://www.sagemath.org/doc/reference/groups/sage/groups/finitely_presented.html

[Will]

I meant to say that I have a presentation for it, though not the one I want.

However, I think I sort of understand how to do this. Namely, I can add a generator, say x, to the given presentation of G, and add the relation x^-1*(...), where "(...)" is what I want the generator to be in terms of the given presentation. Then, I can use TzGo via gap to simplify the presentation, though sometimes TzGo ends up removing the generator I added...