Some power of an element in a Garside group is conjugate to a periodically geodesic element |
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Authors: | Lee, Eon-Kyung Lee, Sang-Jin |
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Affiliation: | Department of Applied Mathematics Sejong University Seoul 143-747 Republic of Korea |
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Abstract: | We show that for each element g of a Garside group, there existsa positive integer m such that gm is conjugate to a periodicallygeodesic element h, an element with |hn| = |n| · |h|for all integers n, where |g| denotes the shortest word lengthof g with respect to the set of simple elements. We also showthat there is a finite-time algorithm that computes, given anelement of a Garside group, its stable super summit set. |
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