Higman group

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In mathematics, the Higman group, introduced by Graham Higman (1951), was the first example of an infinite finitely presented group with no non-trivial finite quotients. The quotient by the maximal proper normal subgroup is a finitely generated infinite simple group. Higman (1974) later found some finitely presented infinite groups Gn,r that are simple if n is even and have a simple subgroup of index 2 if n is odd, one of which is one of the Thompson groups.

Higman's group is generated by 4 elements a, b, c, d with the relations

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