[GAP Forum] Parker loop

[Marek Mitros]

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