| Issue |
RAIRO-Theor. Inf. Appl.
Volume 42, Number 2, April-June 2008
|
|
|---|---|---|
| Page(s) | 395 - 414 | |
| DOI | https://doi.org/10.1051/ita:2007040 | |
| Published online | 20 December 2007 | |
On an algorithm to decide whether a free group is a free factor of another
1
Centro de Matemática, Faculdade de Ciências,
Universidade do Porto, R. Campo Alegre 687, 4169-007 Porto,
Portugal; pvsilva@fc.up.pt
2
LaBRI, CNRS, 351 cours de la Libération, 33405 Talence
Cedex, France; pascal.weil@labri.fr
Received:
25
January
2005
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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