GroupsWithPropertyT/groups/caprace.jl

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struct CapraceGroup <: GAPGroup
args::Dict{String,Any}
end
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name(G::CapraceGroup) = "CapraceGroup"
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function group(G::CapraceGroup)
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caprace_group = Groups.FPGroup(["x","y","z","t","r"])
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x,y,z,t,r = gens(caprace_group)
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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]]
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Groups.add_rels!(caprace_group, Dict(rel => caprace_group() for rel in relations))
return caprace_group
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end