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  "body": "\n## Summary\n\nIn mathematics, the **Higman group**, introduced by (txt), was the first example of an infinite finitely presented group with no [[nontrivial|0BNPC9850Y]] finite [[quotients|0KYX2N69J0]]. The quotient by the maximal proper [[normal subgroup|0CB0DX5BVV]] is a [[finitely generated|082DWWXMRJ]] infinite [[simple group|0C093D1T4M]]. (Higman 1974) later found some finitely presented infinite groups $G_{n,r}$ that are simple if $n$ is even and have a simple [[subgroup|0X1JXT47GA]] of [[index|0DTXBQPA2S]] 2 if $n$ is odd, one of which is one of the Thompson groups.\n",
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