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

A survey of recent results about profinite groups, and results about infinite and finite groups where the theory of profinite groups plays a leading role.

In this short article, we give a summary of the Sylow $p$-subgroups of the finite simple groups of classical Lie type.

In this paper we study arithmetical and structural features of a finite group that possesses exactly two conjugacy class sizes that are composite numbers.

These notes are devoted to lattices in products of trees and related topics. They provide an introduction to the construction, by M. Burger and S. Mozes, of examples of such lattices that are simple as abstract groups. Two features of that…

For a number field K, we show that any S-arithmetic subgroup of SL_2(K) contains a subgroup of finite index generated by three elements if card(S)> 1.

Let $\text{AGL}(1,\Bbb F_q)$ denote the affine linear group of dimension one over the finite field $\Bbb F_q$. We determine the M\"obius function of the lattice of subgroups of $\text{AGL}(1,\Bbb F_q)$.

We compute Euler characteristics of p-subgroup categories of finite groups

We construct K(\pi, 1)'s for Artin groups of type C_n and D_n.

In this paper, we give the enumeration of z-classes in finite Coxeter groups.

We develop a practical algorithm to decide whether a finitely generated subgroup of a solvable algebraic group $G$ is arithmetic. This incorporates a procedure to compute a generating set of an arithmetic subgroup of $G$. We also provide a…

In \cite[Problem 72]{Fuchs60} Fuchs asked the following question: which groups can be the group of units of a commutative ring? In the following years, some partial answers have been given to this question in particular cases. The aim of…

We prove that finite index subgroups in S-arithmetic Chevalley groups are bounded.

In this article, I study some classes of finitely presented groups with the aim of finding out whether the maximal metabelian quotients of the members of these classes admit finite presentations. The considered classes include those of…

Gr\"obner bases of binomial ideals arising from finite lattices will be studied. In terms of Gr\"obner bases and initial ideals, a characterization of finite distributive lattices as well as planar distributive lattices will be given.

We consider one-plaquette unitary matrix model at finite $N$ using exact expression of the partition function for both SU($N$) and U($N$) groups.

Let G be a lattice in PSL(2,C). The pro-normal topology on G is defined by taking all cosets of non-trivial normal subgroups as a basis. This topology is finer than the pro-finite topology, but it is not discrete. We prove that every…

In this short note, we describe the finite groups $G$ having $|G|-1$ cyclic subgroups. This leads to a nice characterization of the symmetric group $S_3$.

Let $G$ be a finite group, define $I(G)=\{x\in G : x^{2}=1\}$, $C(G)=$ set of the cyclic subgroups of $G$, $i(G)=|I(G)|$ and $c(G)=|C(G)|$. In this article, we will classify finite groups with $i(G)=c(G)-r$ for $r=0,1,$ and $2$. We also…

Finite fields form an important chapter in abstract algebra, and mathematics in general. We aim to provide a geometric and intuitive model for finite fields, involving algebraic numbers, in order to make them accessible and interesting to a…

Using generating functions, we enumerate regular semisimple conjugacy classes in the finite classical groups. For the general linear, unitary, and symplectic groups this gives a different approach to known results; for the special…