Cyclically reduced sequence in an HNN extension
= Cyclically reduced sequence in an HNN extension
A cyclically reduced sequence has no <pinch in an HNN extension> either internally or across its cyclic junction. If its stable-letter length is positive, every positive power remains reduced, so <Britton's lemma> gives infinite order. Repeated cyclic conjugation and pinch removal shows that any finite-order element of an <HNN extension> is conjugate into its base <group>.