GroupsWithPropertyT/groups/caprace.jl

struct CapraceGroup <: GAPGroup end

name(G::CapraceGroup) = "CapraceGroup"

function group(G::CapraceGroup)

   caprace_group = Groups.FPGroup(["x","y","z","t","r"])

   x,y,z,t,r = gens(caprace_group)

   relations = [
   x^7,
   y^7,
   t^2,
   r^73,
   t*r*t*r,
   Comm(x,y)*z^-1,
   Comm(x,z),
   Comm(y,z),
   Comm(x^2*y*z^-1, t),
   Comm(x*y*z^3, t*r),
   Comm(x^3*y*z^2, t*r^17),
   Comm(x, t*r^-34),
   Comm(y, t*r^-32),
   Comm(z, t*r^-29),
   Comm(x^-2*y*z, t*r^-25),
   Comm(x^-1*y*z^-3, t*r^-19),
   Comm(x^-3*y*z^-2, t*r^-11)
   ];

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

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