Garside groups are strongly translation discrete
نویسندگان
چکیده
منابع مشابه
Garside Groups Are Strongly Translation Discrete
In this paper we show that all Garside groups are strongly translation discrete, that is, the translation numbers of non-torsion elements are strictly positive and for any real number r there are only finitely many conjugacy classes of elements whose translation numbers are less than or equal to r. It is a consequence of the inequality “infs(g) 6 infs(g n) n < infs(g) + 1” for a positive intege...
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A Garside monoid is a cancellative monoid with a finite lattice generating set; a Garside group is the group of fractions of a Garside monoid. The family of Garside groups contains the Artin-Tits groups of spherical type. We generalise the well-known notion of a parabolic subgroup of an Artin-Tits group into that of a parabolic subgroup of a Garside group. We also define the more general notion...
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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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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2007
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2006.03.018