Dear Timm, Dear Forum, I have some code on GitHub <https://github.com/jwiverson/central-group-frames> that can help construct what Higman calls A(n,theta) in this paper <https://projecteuclid.org/download/pdf_1/euclid.ijm/1255637483>. This is a special example of what we call "B-products" in Section 4 of this paper <https://arxiv.org/abs/1609.09836>.
To make A(n,theta), download the file "b-prods.g" and put it where GAP can find it. Then type something like the following: gap> Read("b-prods.g"); gap> n:=3; 3 gap> theta:=FrobeniusAutomorphism(GF(2^n)); FrobeniusAutomorphism( GF(2^3) ) gap> B:=function(x,y) > return x*y^theta; > end; function( x, y ) ... end gap> G:=bGroup(n,B); <pc group of size 64 with 6 generators> You can replace n and theta with anything want. The result is a pc group. The function "bEmbed" can help you map a pair of field elements (x,y) into G, as in Higman's paper: gap> emb:=bEmbed(B,G,n); function( x, y ) ... end gap> x:=Random(GF(2^n)); Z(2)^0 gap> y:=Random(GF(2^n)); Z(2^3) gap> g:=emb(x,y); f1*f5 I hope this helps! All the best, Joey Iverson Research Associate Norbert Wiener Center & Department of Mathematics University of Maryland, College Park On Thu, Sep 21, 2017 at 11:26 AM, Timm von Puttkamer <tv...@gmx.net> wrote: > Dear all, > > I would like to know whether GAP has a method to construct Suzuki > 2-groups. Recall that a Suzuki 2-group is a non-abelian 2-group containing > more than one involution which admits a cyclic group of automorphims that > acts transitively on the set of involutions. > > Kind regards, > Timm > > > _______________________________________________ > Forum mailing list > Forum@mail.gap-system.org > http://mail.gap-system.org/mailman/listinfo/forum > _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum