Conjugacy in Garside groups III: Periodic braids
نویسندگان
چکیده
منابع مشابه
Subgroup conjugacy problem for Garside subgroups of Garside groups
We solve the subgroup conjugacy problem for parabolic subgroups and Garside subgroups of a Garside group, and we present deterministic algorithms. This solution may be improved by using minimal simple elements. For standard parabolic subgroups of Garside groups we provide e ective algorithms for computing minimal simple elements.
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The cycling operation endows the super summit set Sx of any element x of a Garside group G with the structure of a directed graph Γx. We establish that the subset Ux of Sx consisting of the circuits of Γx can be used instead of Sx for deciding conjugacy to x in G, yielding a faster and more practical solution to the conjugacy problem for Garside groups. Moreover, we present a probabilistic appr...
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Let G be a Garside group with Garside element ∆. An element g ∈ G is said to be periodic with respect to ∆ if some power of g lies in the cyclic group generated by ∆. This paper shows the following. (i) The periodicity of an element does not depend on the choice of a particular Garside structure if and only if the center of G is cyclic. (ii) If g = ∆ for some nonzero integer k, then g is conjug...
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1 We present a solution to the conjugacy decision problem and the conjugacy search problem 2 in Garside groups, which is theoretically simpler than the usual one, with no loss of efficiency. 3 This is done by replacing the well known cycling and decycling operations by a new one, 4 called cyclic sliding, which appears to be a more natural choice. 5 We give an analysis of the complexity of our a...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2007
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2007.02.002