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

Pedro V. Silva; Pascal Weil

RAIRO - Theoretical Informatics and Applications (2007)

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

Abstract

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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.

How to cite

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Silva, 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 42.2 (2007): 395-414. <http://eudml.org/doc/92878>.

@article{Silva2007,
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},
keywords = {Combinatorial group theory; free groups; free factors; inverse automata; algorithms; free factor groups; inverse automata; finitely generated subgroups; lengths of generators; ranks},
language = {eng},
month = {12},
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/92878},
volume = {42},
year = {2007},
}

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
DA - 2007/12//
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; inverse automata; finitely generated subgroups; lengths of generators; ranks
UR - http://eudml.org/doc/92878
ER -

References

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