2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/222013In this paper, we generalize the Shirshov's Composition Lemma by replacing the monomial order for others. By using Groebner-Shirshov bases, the normal forms of HNN extension of a group and the alternating group are obtained.Group Theory20E06, 16S15, 13P10Groebner-Shirshov basis for HNN extensions of groups and for the alternating grouptext