GroupsWithPropertyT/groups/higman.jl

struct HigmanGroup <: GAPGroup end

name(G::HigmanGroup) = "HigmanGroup"

function group(G::HigmanGroup)

   higman_group = Groups.FPGroup(["a","b","c","d"]);

   a,b,c,d = gens(higman_group)

   relations = [
   b*Comm(b,a),
   c*Comm(c,b),
   d*Comm(d,c),
   a*Comm(a,d)
   ];

   relations = [relations; [inv(rel) for rel in relations]]

   Groups.add_rels!(higman_group, Dict(rel => higman_group() for rel in relations))
   return higman_group
end