2026-04-17T01:59:57Zhttps://recercat.cat/oai/request

oai:recercat.cat:2072/4630472026-04-08T07:14:22Zcom_2072_98col_2072_378192

00925njm 22002777a 4500 dc Delgado Rodríguez, Jordi author Ventura, Enric author 2022 We extend the classical Stallings theory (describing subgroups of free groups as automata) to direct products of free and abelian groups: after introducing enriched automata (i.e., automata with extra abelian labels), we obtain an explicit bijection between subgroups and a certain type of such enriched automata, which-as it happens in the free group-is computable in the finitely generated case. This approach provides a neat geometric description of (even non-(finitely generated)) intersections of finitely generated subgroups within this non-Howson family. In particular, we give a geometric solution to the subgroup intersection problem and the finite index problem, providing recursive bases and transversals, respectively. Free group Free-abelian group Direct product Subgroup Intersection Stallings Automata Stallings automata for free-times-abelian groups : intersections and index