Abstract
We study the problem of extracting roots in Garside groups by reducing it to the calculation of certain ultra summit sets. Several properties concerning the roots and an effective algorithm are derived. In particular, in the case of braid groups, a conjecture on the bound of super summit set implies that, for fixed number of strands and ordinal number of root, the algorithm is polynomial in the word length.
ACKNOWLEDGMENTS
Research partially supported by a MOEC grant and a MOSTC grant. The author is grateful to the referee for the notification of recent developments on ultra summit set.
Notes
Communicated by A. Olshanskiy.