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m -medial n -quasigroups

Tomáš Kepka (1991)

Commentationes Mathematicae Universitatis Carolinae

For n ≥ 4 , every n -medial n -quasigroup is medial. If 1 ≤ m < n , then there exist m -medial n -quasigroups which are not ( m + 1 ) -medial.

Macdonald formula for spherical functions on affine buildings

A. M. Mantero, A. Zappa (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

In this paper we explicitly determine the Macdonald formula for spherical functions on any locally finite, regular and affine Bruhat-Tits building, by constructing the finite difference equations that must be satisfied and explaining how they arise, by only using the geometric properties of the building.

Malnormal subgroups and Frobenius groups: basics and examples

Pierre de la Harpe, Claude Weber (2014)

Confluentes Mathematici

Malnormal subgroups occur in various contexts. We review a large number of examples, and compare the general situation to that of finite Frobenius groups of permutations.In a companion paper [18], we analyse when peripheral subgroups of knot groups and 3 -manifold groups are malnormal.

Manin’s and Peyre’s conjectures on rational points and adelic mixing

Alex Gorodnik, François Maucourant, Hee Oh (2008)

Annales scientifiques de l'École Normale Supérieure

Let X be the wonderful compactification of a connected adjoint semisimple group G defined over a number field K . We prove Manin’s conjecture on the asymptotic (as T → ∞ ) of the number of K -rational points of X of height less than T , and give an explicit construction of a measure on X ( 𝔸 ) , generalizing Peyre’s measure, which describes the asymptotic distribution of the rational points 𝐆 ( K ) on X ( 𝔸 ) . Our approach is based on the mixing property of L 2 ( 𝐆 ( K ) ∖ 𝐆 ( 𝔸 ) ) which we obtain with a rate of convergence.

Mapping class group of a handlebody

Bronisław Wajnryb (1998)

Fundamenta Mathematicae

Let B be a 3-dimensional handlebody of genus g. Let ℳ be the group of the isotopy classes of orientation preserving homeomorphisms of B. We construct a 2-dimensional simplicial complex X, connected and simply-connected, on which ℳ acts by simplicial transformations and has only a finite number of orbits. From this action we derive an explicit finite presentation of ℳ.

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