Higman group

Template:For In mathematics, the Higman group, introduced by Template:Harvs, was the first example of an infinite finitely presented group with no nontrivial finite quotients. The quotient by the maximal proper normal subgroup is a finitely generated infinite simple group. Template:Harvtxt later found some finitely presented infinite groups Template:Math that are simple if Template:Math is even and have a simple subgroup of index 2 if Template:Math is odd, one of which is one of the Thompson groups.

Higman's group is generated by 4 elements Template:Math with the relations

$a^{-1}ba=b^2,b^{-1}cb=c^2,c^{-1}dc=d^2,d^{-1}ad=a^2.$

References

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