On an algorithm to decide whether a free group is a free factor of another

Pedro Silva (1) , Pascal Weil (2)

1 CMUP - Centro de Matemática, Faculdade de Ciências
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique

We revisit the problem of deciding whether a finitely generated subgroup H is a free factor of a given free group F. Known algorithms solve this problem in time polynomial in the sum of the lengths of the generators of H and exponential in the rank of F. We show that the latter dependency can be made exponential in the rank difference rank(F) - rank(H), which often makes a significant change.

Mots clés: combinatorial group theory; free groups; free factors; inverse automata; algorithms

Domaines: Théorie des groupes [math.GR]

Pedro Silva, Pascal Weil. On an algorithm to decide whether a free group is a free factor of another. RAIRO - Theoretical Informatics and Applications (RAIRO: ITA), 2008, 42, pp.395-414. ⟨hal-00096810v2⟩