Silva, Pedro V.; Weil, Pascal
On an algorithm to decide whether a free group is a free factor of another
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 2 , p. 395-414
Zbl 1146.20021 | MR 2401269
doi : 10.1051/ita:2007040
URL stable : http://www.numdam.org/item?id=ITA_2008__42_2_395_0

Classification:  20E05,  05C25
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.

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