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

Published online by Cambridge University Press:  20 December 2007

Pedro V. Silva  and
Pascal Weil
Pedro V. Silva
Affiliation:
Centro de Matemática, Faculdade de Ciências, Universidade do Porto, R. Campo Alegre 687, 4169-007 Porto, Portugal; pvsilva@fc.up.pt
Pascal Weil
Affiliation:
LaBRI, CNRS, 351 cours de la Libération, 33405 Talence Cedex, France; pascal.weil@labri.fr
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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.

Keywords

Combinatorial group theoryfree groupsfree factorsinverse automataalgorithms
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 42 , Issue 2 , April 2008 , pp. 395 - 414
Copyright
© EDP Sciences, 2007

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