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

Pedro Silva·Pascal Weil
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Abstract

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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Pedro Silva, Pascal Weil. 2006-11-16. On an algorithm to decide whether a free group is a free factor of another. https://arxiv.org/abs/math/0609552

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