Conjugacy in Garside groups III: Periodic braids

摘要: Abstract An element in Artin's braid group B n is said to be periodic if some power of it lies the center . In this paper we prove that all previously known algorithms for solving conjugacy search problem are exponential index special case braids. We overcome difficulty by putting work several isomorphisms between Garside structures and other groups. This allows us obtain a polynomial solution original spirit algorithms. third series papers same authors about They have unified goal: development algorithm decision problems , which generalizes groups whenever possible. It our hope methods introduced here will allow generalization results Artin–Tits spherical type.