Pinch in an HNN extension
= Pinch in an HNN extension
{title2=$tat^{-1},\ t^{-1}bt$}
= Pinches in an HNN extension
{synonym}
In $\langle G,t\mid tat^{-1}=\phi(a),\ a\in A\rangle$, a pinch is a subword $tat^{-1}$ with $a\in A$, or $t^{-1}bt$ with $b\in B=\phi(A)$. It can be replaced by a base-group element, removing two stable letters. <Britton's lemma> asserts that every identity word with stable letters must have a pinch after base-group multiplication is performed.