Related papers: Finite subgroups of arithmetic lattices in U(2,1)

In this note we study the finite groups whose subgroup lattices are dismantlable.

The main goal of this paper is to apply the arithmetic method developed in our previous paper \cite{13} to determine the number of some types of subgroups of finite abelian groups.

In this paper we give a description of the possible limit sets of finitely generated subgroups of irreducible lattices in $PSL(2,R)^r$.

In this article we introduce and study a class of finite groups for which the orders of normal subgroups satisfy a certain inequality. It is closely connected to some well-known arithmetic classes of natural numbers.

We show that strong approximate lattices in higher-rank semi-simple algebraic groups are arithmetic.

This article describes a practical approach for determining the lattice of subgroups U < V < G between given subgroups U and G, provided the total number of such subgroups is not too large. It builds on existing functionality for element…

In this paper, we determine the genus of the subgroup lattice of several families of abelian groups. In doing so, we classify all finite abelian groups whose subgroup lattices can be embedded into the torus.

We characterize the finite intervals of the Muchnik lattice by proving that they are a certain proper subclass of the finite distributive lattices.

We announce an atlas of subgroup lattices of almost simple groups and present two algorithms that were used to produce the atlas.

T.C. Burness and S.D. Scott \cite{3} classified finite groups $G$ such that the number of prime order subgroups of $G$ is greater than $|G|/2-1$. In this note, we study finite groups $G$ whose subgroup graph contains a vertex of degree…

We show that for a typical high rank arithmetic lattice $\Gamma$, there exist finite index subgroups $\Gamma_{1}$ and $\Gamma_{2}$ such that $\Gamma_{1} \not\simeq \Gamma_{2}$ while $\widehat{\Gamma_{1}} \simeq \widehat{\Gamma_{2}}$. But…

We classify, up to conjugacy, the finite subgroups of PGL(2,K) of order prime to char(K).

For a finite group G, we denote by v(G) the number of conjugacy classes of subgroups of G not in CD(G). In this paper, we determine the finite groups G such that v(G)=1,2,3.

We determine many of the atoms of the algebraic lattices arising in $\mathfrak{q}$-theory of finite semigroups.

In this paper we use techniques from convex projective geometry to produce many new examples of thin subgroups of lattices in special linear groups that are isomorphic to the fundamental groups of finite volume hyperbolic manifolds. More…

Let $G$ be a real Lie group and $\Gamma < G$ be a discrete subgroup of $G$. Is $\Gamma$ residually finite? This paper describes known positive and negative results then poses some questions whose answers will lead to a fairly complete…

In this paper we introduce and study the lattice of normal subgroups of a group $G$ that determine solitary quotients. It is closely connected to the well-known lattice of solitary subgroups of $G$ (see \cite{5}). A precise description of…

In this note we describe the finite groups $G$ having $|G|-2$ cyclic subgroups. This partially solves the open problem in the end of \cite{3}.

Given a finite group $G$, we denote by $L(G)$ the subgroup lattice of $G$ and by ${\cal CD}(G)$ the Chermak-Delgado lattice of $G$. In this note, we determine the finite groups $G$ such that $|{\cal CD}(G)|=|L(G)|-k$, $k=1,2$.

Let $A$ be an Artin algebra. We investigate subalgebras of $A$ with certain conditions and obtain some classes of algebras whose finitistic dimensions are finite.