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

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2008)

- Volume: 42, Issue: 2, page 395-414
- ISSN: 0988-3754

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topSilva, Pedro V., and 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 42.2 (2008): 395-414. <http://eudml.org/doc/245285>.

@article{Silva2008,

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.},

author = {Silva, Pedro V., Weil, Pascal},

journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},

keywords = {combinatorial group theory; free groups; free factors; inverse automata; algorithms; free factor groups; finitely generated subgroups; lengths of generators; ranks},

language = {eng},

number = {2},

pages = {395-414},

publisher = {EDP-Sciences},

title = {On an algorithm to decide whether a free group is a free factor of another},

url = {http://eudml.org/doc/245285},

volume = {42},

year = {2008},

}

TY - JOUR

AU - Silva, Pedro V.

AU - Weil, Pascal

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

JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

PY - 2008

PB - EDP-Sciences

VL - 42

IS - 2

SP - 395

EP - 414

AB - 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.

LA - eng

KW - combinatorial group theory; free groups; free factors; inverse automata; algorithms; free factor groups; finitely generated subgroups; lengths of generators; ranks

UR - http://eudml.org/doc/245285

ER -

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