= Higman group as an amalgam of iterated HNN extensions
{c}
{title2=$\langle a,b,c,d\mid a^{-1}ba=b^2,\ b^{-1}cb=c^2,\ c^{-1}dc=d^2,\ d^{-1}ad=a^2\rangle$}
The two three-generator components on $\{a,b,c\}$ and $\{c,d,a\}$ are iterated <HNN extensions> of infinite cyclic groups. The subgroup on $\{a,c\}$ is free of rank two in each component by <Britton's lemma>. Amalgamating over these free subgroups gives the displayed infinite <finitely presented group>. Its cyclic squaring relations forbid every nontrivial finite quotient by the least-prime multiplicative-order argument.
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