50 lines
1020 B
Julia
50 lines
1020 B
Julia
module HigmanGroup
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using AbstractAlgebra
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using Groups
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###############################################################################
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#
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# Generating set
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#
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###############################################################################
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Comm(x,y) = x*y*x^-1*y^-1
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function generatingset()
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HigmanGr = Groups.FPGroup(["a","b","c","d"]);
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a,b,c,d = gens(HigmanGr)
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relations = [
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b^-1*Comm(b,a),
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c^-1*Comm(c,b),
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d^-1*Comm(d,c),
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a^-1*Comm(a,d)
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];
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relations = [relations; [inv(rel) for rel in relations]]
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Groups.add_rels!(HigmanGr, Dict(rel => HigmanGr() for rel in relations))
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return HigmanGr, gens(HigmanGr)
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end
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function generatingset(parsed_args)
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return generatingset()
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end
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###############################################################################
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#
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# Misc
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#
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###############################################################################
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function groupname(parsed_args)
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return groupname(), 0
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end
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groupname() = "HigmanGroup"
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end # of module CapraceGroup
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