[GAP Forum] Reduction of elements of FpGroup

[Stephen Linton]

Dear Gaurav Dhingra,

Firstly, I’m afraid there is no standard meaning of “small” in GAP. This is simply a comment by the
developer of this routine to explain what the next few lines are doing.

In fact we can see from the next lines that the test is whether the group can be seen to have order less than 50000. That is whether a faithful homomorphism is known, or can be found (FPFaithHom) and if so whether the image has order < 50000.

This information is used to choose between two different ways of reducing the element to normal form. For “small” groups 
the work is done in Factorisation which produces short words and is quick for small groups but can be very slow for larger ones. For larger groups a more sophisticated method is used, which may produce longer normal words, and requires quite a lot of setup but can be much faster for very large groups.

	Steve



> On 19 Mar 2016, at 06:31, Gaurav Dhingra <axyd0000 at gmail.com> wrote:
> 
> Hi GAP forum members,
> 
> I am looking at the source code `FpElementNFFunction` (no documentation for it), in that there is a comment
> ```
> # first try whether the group is ``small''
> ```
> 
> what does "small" means in GAP terms? Is this some standard jargon used in GAP source code? If so how is this used internally? It will be helpful if you could explain this used in a little deail.
> I believe GAP uses somehow "small" group to refer to groups below certain "order", if this is the case. To what things it makes things useful?
> 
> Thank you
> Gaurav
> 
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