Explore: Representations Of Congruence Lattices

distributive lattices with ℵ2 compact elements using a construction based on Kuratowski's free set theorem. We denote by Con A the congruence lattice of an algebra

In mathematics, a congruence subgroup of a matrix group with integer entries is a subgroup defined by congruence conditions on the entries. A very simple

congruence classes: [u]~ ∘ [v]~ = [uv]~ Because ~ is a congruence, the set of all congruence classes of ~ forms a semigroup with ∘, called the quotient semigroup

σ is a congruence and, in fact, it is a group congruence, meaning that the factor semigroup S/σ is a group. In the set of all group congruences on a semigroup

video at right. Important subgroups of the modular group Γ, called congruence subgroups, are given by imposing congruence relations on the associated matrices

(T). By Kazhdan's theorem, lattices in this group have property (T). This construction is significant because these lattices are hyperbolic groups; thus

analogous result that concerns congruence relations instead of normal subgroups holds for any algebraic structure. Modular lattice Derek John Scott Robinson

Institute of Mathematics of the Hebrew University of Jerusalem. He is known for contributions to geometric group theory, the study of lattices in Lie groups

phenomenon where families of mock modular forms appear to be attached to Niemeier lattices. The special case of the A24 1 lattice yields Mathieu Moonshine

pattern; classification; scaling; position; congruence; area; perimeter. Two-dimensional representations of the geoboard may be applied to ordinary paper