RAIRO-Theor. Inf. Appl.
Volume 42, Number 2, April-June 2008
|Page(s)||395 - 414|
|Published online||20 December 2007|
On an algorithm to decide whether a free group is a free factor of another
Centro de Matemática, Faculdade de Ciências,
Universidade do Porto, R. Campo Alegre 687, 4169-007 Porto,
2 LaBRI, CNRS, 351 cours de la Libération, 33405 Talence Cedex, France; email@example.com
Accepted: 8 October 2007
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.
Mathematics Subject Classification: 20E05 / 05C25
Key words: Combinatorial group theory / free groups / free factors / inverse automata / algorithms
© EDP Sciences, 2007
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