Related papers: Finite groups in integral group rings

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

In 1996 Jespers and Wang classified finite semigroups whose integral semigroup ring has finitely many units. In a recent paper, Iwaki-Juriaans-Souza Filho continued this line of research by partially classifying the finite semigroups whose…

These are notes of lectures given at UN Encuentro 2016 at the Colombia National University. We begin with the definition of infinite $W$-algebras. Then we explain the motivation for the definition if finite $W$-algebras. Then we present…

We study those group rings whose group of units is hyperbolic.

We classify the finite groups $G$ such that the group of units of the integral group ring ${\mathbb Z} G$ has a subgroup of finite index which is a direct product of free-by-free groups.

We survey some results concerning finite group actions on products of spheres.

This is a summary of the material for 3 lectures on geometrically finite and infinite Kleinian groups delivered by the author at a workshop held at Tata Institute of Fundamental Research in April 2014.

We present an exposition of our ongoing project in a new area of applicable mathematics: practical computation with finitely generated linear groups over infinite fields. Methodology and algorithms available for practical computation in…

We present an overview of the theory of finite groups, with regard to their application as flavour symmetries in particle physics. In a general part, we discuss useful theorems concerning group structure, conjugacy classes, representations…

On June 5, 2007 the second author delivered a talk at the Journees de l'Institut Elie Cartan entitled "Finite symmetry groups in complex geometry". This paper begins with an expanded version of that talk which, in the spirit of the…

This paper continues the study of Fourier transforms on finite inverse semigroups, with a focus on Fourier inversion theorems and FFTs for new classes of inverse semigroups. We begin by introducing four inverse semigroup generalizations of…

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.

Which groups can occur as the group of units in a ring? Such groups are called realizable. Though the realizable members of several classes of groups have been determined (e.g., cyclic, odd order, alternating, symmetric, finite simple,…

These notes give a short introduction to finite Coxeter groups, their classification, and some parts of their representation theory, with a focus on the infinite families. They are based on lectures delivered by the author at the…

The structure of groups for which certain sets of commutator subgroups are finite is investigated, with a particular focus on the relationship between these groups and those with finite derived subgroup.

We investigate the finite subgroups that occur in the Hamiltonian quaternion algebra over the real subfield of cyclotomic fields. When possible, we investigate their distribution among the maximal orders.

We determine the finite groups whose real irreducible representations have different degrees.

In 1960 Fuchs posed the problem of characterizing the groups which are the groups of units of commutative rings. In the following years, some partial answers have been given to this question in particular cases. In this paper we address…

In this paper we first survey some basic results in the cohomology of finite groups, and then discuss recent work on constructing free actions of finite groups on products of spheres.

Sorin Popa initiated the study of Polish groups which are embeddable into the unitary group of a separable finite von Neumann algebra. Such groups are called of finite type. We give necessary and sufficient conditions for Polish groups to…