Stable Super Summit Sets in Garside Groups
نویسندگان
چکیده
The known algorithms for solving the conjugacy problem in Garside groups involve computing a particular subset of the conjugacy class, the so-called super summit set. The super summit set [g] of an element g in a Garside group is, intuitively, the set of all conjugates of g that have the shortest normal form in the conjugacy class of g. In this paper, we define the stable super summit set [g] of g as the set of all conjugates h of g such that h ∈ [g] for all n > 1, in other words, all the powers h have the shortest normal form in the conjugacy class of g. We show that every stable super summit set is nonempty and satisfies most of the nice properties of the super summit set.
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