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

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

2006-09-20

arxiv.org/abs/math/0609552v2

Theoretical Informatics and Applications 42 (2008) 395-414

Mathematics

Group Theory

20 pages

Scientific paper

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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