[GAP Forum] Parker loop

[Stephen Linton]

I started trying to automatise this construction some years ago. I recall that I got as far as constructing Fi24 in characteristic zero 
by these methods. I don't know if I still have any of the code I wrote, let alone whether it works with current GAP.
I'll have a look.

	Steve

On 2 Dec 2011, at 10:52, Marek Mitros wrote:

> Hi All,
> 
> I am reading Conway "simple construction of monster" and I wonder whether
> anybody has Parker loop defined for GAP. I would like to play around with
> it to understand more how multiplication there looks like.
> For example when I have two octads o1, o2 intersecting in four points then
> let o3 be XOR(o1,o2). Then I assume that in Parker loop o1.o2=o3, o2.o3=o1,
> etc and all these products commutes.
> When I have octads o1,o2 intersecting in two points then d1=XOR(o1,o2) is
> dodecad. In such case I do not know whether o1.o2=d1 or o1.o2=-d1 (minus).
> In such case product o1.o2 anticommute.
> 
> The next question I have is how to generate extraspecial group of size 2^25
> called Q_x1 in the paper. It is generated by elements x_d and x_delta.
> 
> Regards,
> Marek
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