منابع مشابه
Algebraic Monoids and Group Embeddings
We study the geometry of algebraic monoids. We prove that the group of invertible elements of an irreducible algebraic monoid is an algebraic group, open in the monoid. Moreover, if this group is reductive, then the monoid is affine. We then give a combinatorial classification of reductive monoids by means of the theory of spherical varieties.
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We study commutation properties of subsets of right-angled Artin groups and trace monoids. We show that if Γ is any graph not containing a four-cycle without chords, then the group G(Γ) does not contain four elements whose commutation graph is a four-cycle; a consequence is that G(Γ) does not have a subgroup isomorphic to a direct product of non-abelian free groups. We also obtain corresponding...
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We use a new version of the Definability Theorem of Beth in order to unify classical Theorems of Yuri Matiyasevich and Jan Denef in one structural statement. We give similar forms for other important definability results from Arithmetic and Number Theory. A.M.S. Classification: Primary 03B99; Secondary 11D99.
متن کاملGarside monoids vs divisibility monoids
Divisibility monoids (resp. Garside monoids) are a natural algebraic generalization of Mazurkiewicz trace monoids (resp. spherical Artin monoids), namely monoids in which the distributivity of the underlying lattices (resp. the existence of common multiples) is kept as an hypothesis, but the relations between the generators are not supposed to necessarily be commutations (resp. be of Coxeter ty...
متن کاملExperiments in Coset Enumeration
Coset enumeration, based on the methods described by Todd and Coxeter, is one of the most important tools for investigating nitely presented groups. Such methods do not, in general, constitute an algorithm. Each problem has to be addressed individually, and determining whether or not an acceptable solution for a diicult problem can be found using given resources requires an empirical approach (...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 2008
ISSN: 1446-7887,1446-8107
DOI: 10.1017/s1446788708000153