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

We show that all the currently known non-arithmetic lattices in ${\rm PU}(2,1)$ are monodromy groups of higher hypergeometric functions.

We define a class of finite groups based on the properties of the closed twins of their power graphs and study the structure of those groups. As a byproduct, we obtain results about finite groups admitting a partition by cyclic subgroups.

Given a group $G$ and a subgroup $H$, we let $\mathcal{O}_G(H)$ denote the lattice of subgroups of $G$ containing $H$. This paper provides a classification of the subgroups $H$ of $G$ such that $\mathcal{O}_{G}(H)$ is Boolean of rank at…

We classify the finite groups whose non-linear irreducible characters that are not conjugate under the natural Galois action have distinct degrees, therefore extending the results in Berkovich et al. [Proc. Amer. Math. Soc. {\bf 115}…

We obtain an infinite family of orthogonal hypergeometric groups, which are higher rank arithmetic groups. We also list cases of arithmetic hypergeometric groups whose real Zariski closure is O(2,3).

We survey the existing parts of a classification of finite groups generated by orthogonal transformations in a finite-dimensional Euclidean space whose fixed point subspace has codimension one or two and extend it to a complete…

In this note we determine the finite groups that can be written as the union of any three irredundant/distinct proper subgroups. The finite groups that can uniquely be written as the union of three proper subgroups are also characterized.

We describe here the lower garland of some lattices of intermediate subgroups in linear groups. The results are applied to the case of subgroup lattices in general and special linear groups over a class of rings, containing the group of…

In this paper, we explain the importance of finite decomposition semigroups and present two theorems related to their structure.

Let G be a unipotent algebraic subgroup of some GL_m(C) defined over Q. We describe an algorithm for finding a finite set of generators of the subgroup G(Z) = G \cap GL_m(Z). This is based on a new proof of the result (in more general form…

We prove in a large number of cases, that a Zariski dense discrete subgroup of a simple real algebraic group $G$ which contains a higher rank lattice is a lattice in the group $G$. For example, we show that a Zariski dense subgroup of…

The well known Andrews-Curtis Conjecture [2] is still open. In this paper, we establish its finite version by describing precisely the connected components of the Andrews-Curtis graphs of finite groups. This finite version has independent…

A complete list of one dimensional groups definable in the p-adic numbers is given, up to a finite index subroup and a quotient by a finite subgroup.

The main goal of the current paper is to determine the total number of diamonds in the subgroup lattice of a finite abelian group. This counting problem is reduced to finite $p$-groups. Explicit formulas are obtained in some particular…

We prove:(1) the existence, for every integer n > 3, of a noncompact smooth n-dimensional topological manifold whose diffeomorphism group contains an isomorphic copy of every finitely presented group; (2) a finiteness theorem on finite…

A group $G$ is said to have dense normalizers if each non-empty open interval in its subgroup lattice $L(G)$ contains the normalizer of a certain subgroup of $G$. In this note, we find all finite groups satisfying this property. We also…

In his paper "Finite groups have many conjugacy classes" (J. London Math. Soc (2) 46 (1992), 239-249), L. Pyber proved the to date best general lower bounds for the number of conjugacy classes of a finite group in terms of the order of the…

In [A. Stolz and A. Thom, On the lattice of normal subgroups in ultraproducts of compact simple groups, PLMS 108(1), 2014] it was stated that the lattice of normal subgroups of an ultraproduct of finite simple groups is always linearly…

We give a structural description of the normal subgroups of subgroups of finite index in branch groups in terms of rigid stabilizers. This gives further insight into the structure lattices of branch groups introduced by the second author.…

We consider a certain hybridization construction which produces a subgroup of ${\rm PU}(n,1)$ from a pair of lattices in ${\rm PU}(n-1,1)$. Among the Picard modular groups ${\rm PU}(2,1,\mathcal{O}_d)$, we show that the hybrid of pairs of…