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

There are errors in the proof of the uniqueness of arithmetic subgroups of the smallest covolume. In this note we correct the proof, obtain certain results which were stated as a conjecture, and we give several remarks on further developments.

In this paper, we study the unimodular equivalence of sublattices in an $n$-dimensional lattice. A recursive procedure is given to compute the cardinalities of the unimodular equivalent classes with the indices which are powers of a prime $p$. We also show that these are integral polynomials in $p$. When $n=2$, the explicit formulae of the cardinalities are presented depending on the prime decomposition of the index $m$. We also give an explicit formula on the number of co-cy...

We use the SmallGroups Library to find the finite subgroups of U(3) of order smaller than 512 which possess a faithful three-dimensional irreducible representation. From the resulting list of groups we extract those groups that can not be written as direct products with cyclic groups. These groups are the basic building blocks for models based on finite subgroups of U(3). All resulting finite subgroups of SU(3) can be identified using the well known list of finite subgroups o...

In this work, we derive the low index subgroups of the extended Hecke, Hecke and the Picard groups using tools in color symmetry theory. We also present the low index subgroups of the modular group.

This paper studies a subset of the free semi-group $F_k$ with letters in a field $k$ which has some interesting arithmetic and combinatorial properties.

We classify abelian subgroups of two-dimensional Artin groups.

A group is LERF (locally extended residually finite) if all its finitely generated subgroups are separable. We prove that the trialitarian arithmetic lattices in $\mathbf{PSO}_{7,1}(\mathbb{R})$ are not LERF. This result, together with previous work by the third author, implies that all arithmetic lattices in $\mathbf{PO}_{n,1}(\mathbb{R})$, $n>3$, are not LERF.

The paper is devoted to the study of the lattice of subgroups of the Lamplighter type groups and to the relative gradient rank.

The Chermak-Delgado lattice of a finite group G is a self-dual sublattice of the subgroup lattice of G. In this paper, we determine finite p-groups with at most p2 + p subgroups not in Chermak-Delgado lattice.

This paper is devoted to the units of integral group rings of cyclic $2$-groups of small orders, namely, the orders of $2^n$ for $n<8$. Immediately we should note the issues our consideration describe in the introduction in more detail. Here we will indicate the main directions of our research. Previously, we proved that the normalized group of units of an integral group ring of a cyclic 2-group of order $2^n$ contains a subgroup of finite index, which is the direct product...