2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/222012In this paper, by using the Groebner-Shirshov bases, we give characterizations of the Schreier extensions of groups when the group is presented by generators and relations. An algorithm to find the conditions of a group to be a Schreier extension is obtained. By introducing a special total order, we obtain the structure of the Schreier extension by an HNN group.Group Theory20E06, 16S15, 13P10text