Abelian Subgroups of Garside Groups Eon-kyung Lee and Sang
نویسنده
چکیده
In this paper, we show that for every abelian subgroup H of a Garside group, some conjugate gHg consists of ultra summit elements and the centralizer of H is a finite index subgroup of the normalizer of H. Combining with the results on translation numbers in Garside groups, we obtain an easy proof of the algebraic flat torus theorem for Garside groups and solve several algorithmic problems concerning abelian subgroups of Garside groups.
منابع مشابه
Translation Numbers in a Garside Group Are Rational with Uniformly Bounded Denominators
It is known that Garside groups are strongly translation discrete. In this paper, we show that the translation numbers in a Garside group are rational with uniformly bounded denominators and can be computed in finite time. As an application, we give solutions to some group-theoretic problems.
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It is known that Garside groups are strongly translation discrete. In this paper, we show that the translation numbers in a Garside group are rational with uniformly bounded denominators and can be computed in finite time. As an application, we give solutions to some group-theoretic problems. 2000 Mathematics Subject Classification: 20F10; 20F36
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