منابع مشابه
Lattices on Non-uniform Trees
Let X be a locally finite tree, and let G = Aut(X). Then G is a locally compact group. We show that if X has more than one end, and if G contains a discrete subgroup Γ such that the quotient graph of groups Γ\\X is infinite but has finite covolume, then G contains a non-uniform lattice, that is, a discrete subgroup Λ such that Λ\G is not compact, yet has a finite G-invariant measure. 0. Notatio...
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In this article, we prove that a lattice of minimum covolume in a simple Lie group over a positive characteristic local field is non-uniform if the Weil’s conjecture on Tamagawa numbers [Wei61] holds. This, in part, answers Lubotzky’s conjecture [Lub91]
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A lattice L is uniform, if for any congruence Θ of L, any two congruence classes A and B of Θ are of the same size, that is, |A| = |B| holds. A classical result of R. P. Dilworth represents a finite distributive lattice D as the congruence lattice of a finite lattice L. We show that this L can be constructed as a finite uniform lattice.
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We study finite residuated lattices with up to 11 elements. We present an algorithm for generating all non-isomorphic finite residuated lattices with a given number of elements. Furthermore, we analyze selected properties of all the lattices generated by our algorithm and present summarizing statistics.
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Abstract. There is a well-known asymptotic formula, due to W. M. Schmidt (1968) for the number of full-rank integer lattices of index at most V in Z. This set of lattices L can naturally be partitioned with respect to the factor group Z/L. Accordingly, we count the number of full-rank integer lattices L ⊆ Z such that Z/L is cyclic and of order at most V , and deduce that these co-cyclic lattice...
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ژورنال
عنوان ژورنال: Israel Journal of Mathematics
سال: 2019
ISSN: 0021-2172,1565-8511
DOI: 10.1007/s11856-019-1868-4