Related papers: Non-residually finite $\tilde{C}_2$-lattices

Equations over linearly ordered semilattices are studied. For any equation $t(X)=s(X)$ we find irreducible components of its solution set and compute the average number of irreducible components of all equations in $n$ variables.

We construct two CW-complexes $K$ and $L$ admitting a common, but not finite common, covering, where $K$ is homeomorphic to a complex with a single 2-cell.

For a class C of finite lattices, the question arises whether any lattice in C can be embedded into some atomistic, biatomic lattice in C. We provide answers to the question above for C being, respectively, --The class of all finite…

We construct three groups $\Lambda_1$, $\Lambda_2$, $\Lambda_3$, which can all be decomposed as amalgamated products $F_9 \ast_{F_{81}} F_{9}$ and have very few normal subgroups of finite or infinite index. Concretely, $\Lambda_1$ is a…

A lattice L is slim if it is finite and the set of its join-irreducible elements contains no three-element antichain. We prove that there exists a positive constant C such that, up to similarity, the number of planar diagrams of these…

We prove that, under mild assumptions, a lattice in a product of semi-simple Lie group and a totally disconnected locally compact group is, in a certain sense, arithmetic. We do not assume the lattice to be finitely generated or the ambient…

We study the smallest, as well as the largest numbers of congruences of lattices of an arbitrary finite cardinality $n$. Continuing the work of Freese and Cz\' edli, we prove that the third, fourth and fifth largest numbers of congruences…

We describe a straightforward construction of the pseudo-split absolutely pseudo-simple groups of minimal type with irreducible root systems of type $BC_n$; these exist only in characteristic $2$. We also give a formula for the dimensions…

We construct the first examples of residually finite amenable groups that are not Hilbert-Schmidt (HS) stable. We construct finitely generated, class 3 nilpotent by cyclic examples and solvable linear finitely presented examples. This also…

We announce various results concerning the structure of compactly generated simple locally compact groups. We introduce a local invariant, called the structure lattice, which consists of commensurability classes of compact subgroups with…

We show that the variety of residuated lattices does not have the amalgamation property, thereby settling a long-standing open problem. In addition, we show that the amalgamation property fails for several subvarieties, including idempotent…

We consider the finitely generated groups acting on a regular tree with almost prescribed local action. We show that these groups embed as cocompact irreducible lattices in some locally compact wreath products. This provides examples of…

We present two uncountable families of finitely generated residually finite groups all having the same profinite completion. One consists of soluble groups, the other of branch groups.

For a modular lattice $L$ of finite length, we prove that the distributivity of $L$ is a sufficient condition while its 2-distributivity is a necessary condition that those sublattices of $L$ that are closed under taking relative…

In residuated binars there are six non-obvious distributivity identities of $\cdot$,$/$,$\backslash$ over $\wedge, \vee$. We show that in residuated binars with distributive lattice reducts there are some dependencies among these…

Since for the classification of finite (congruence-)simple semirings it remains to classify the additively idempotent semirings, we progress on the characterization of finite simple additively idempotent semirings as semirings of…

We consider finite 2-dimensional polyhedral complexes, equipped with piecewise non-positively curved, locally CAT(0) metrics. We give conditions on the complex X that ensure that its fundamental group contains a surface subgroup. Concrete…

A myriad of irreducible symplectic 4-manifolds with abelian non-cyclic fundamental group is constructed. The botany of manifolds with finite non-cyclic fundamental groups is also studied.

We prove a simplicity criterion for certain twin tree lattices. It applies to all rank two Kac-Moody groups over finite fields with non-trivial commutation relations, thereby yielding examples of simple non-uniform lattices in the product…

The sets of primitive, quasiprimitive, and innately transitive permutation groups may each be regarded as the building blocks of finite transitive permutation groups, and are analogues of composition factors for abstract finite groups. This…