Bill Allombert on Tue, 08 Jan 2008 12:59:02 +0100

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Re: GAP4 group names

On Mon, Jan 07, 2008 at 07:07:45PM -0500, Roger Lipsett wrote:
> Can someone tell me where to find the "translation" of the GAP4 group names
> given by PARI as well as GAP4? I've looked on line, and the only reference
> appears to be a book that I don't care to purchase. Neither the GAP4 nor the
> PARI docs seem to contain the algorithm.

The group naming is explained in

> For example, "polgalois(x^8-3)" returns (among other things) [1/4.cD(4)^2]2,
> and polgalois(x^8-2) returns 2D_8(8)=[D(4)]2.

I am not quite sure you mean by algorithm here, but if GP returns e.g.
? polgalois(x^8-3)
%1 = [32, -1, 15, "[1/4.cD(4)^2]2"]

Then you can construct the transitive group under GAP with the command

gap> G:=TransitiveGroup(8,15);

And then perform any computation on G.