Juan González-Meneses

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In this paper a relation between iterated cyclings and iterated powers of elements in a Garside group is shown. This yields a characterization of elements in a Garside group having a rigid power, where 'rigid' means that the left normal form changes only in the obvious way under cycling and decycling. It is also shown that, given X in a Garside group, if(More)
This paper is the second in a series (the others are [2] and [3]) in which the authors study the conjugacy decision problem (CDP) and the conjugacy search problem (CSP) in Garside groups. The ultra summit set U SS(X) of an element X in a Garside group G is a finite set of elements in G, introduced in [14], which is a complete invariant of the conjugacy(More)
We give a new method to compute the centralizer of an element in Artin braid groups and, more generally, in Garside groups. This method, together with the solution of the conjugacy problem given by the authors in [9], are two main steps for solving conjugacy systems, thus breaking recently discovered cryptosystems based in braid groups [2]. We also present(More)
An element in Artin's braid group B n is said to be periodic if some power of it lies in the center of B n. In this paper we prove that all previously known algorithms for solving the conjugacy search problem in B n are exponential in the braid index n for the special case of periodic braids. We overcome this difficulty by putting to work several known(More)