Related papers: Critical groups of group representations

We estimate the proportion of several classes of elements in finite classical groups which are readily recognised algorithmically, and for which some power has a large fixed point subspace and acts irreducibly on a complement of it. The…

This paper defines and develops cycle indices for the finite classical groups. These tools are then applied to study properties of a random matrix chosen uniformly from one of these groups. Properties studied by this technique will include…

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

We present a uniform methodology for computing with finitely generated matrix groups over any infinite field. As one application, we completely solve the problem of deciding finiteness in this class of groups. We also present an algorithm…

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 $S_3$.

Given a prime power $p^d$ with $p$ a prime and $d$ a positive integer, we classify the finite groups $G$ with $p^{2d}$ dividing $|G|$ in which all subgroups of order $p^d$ are complemented and the finite groups $G$ having a normal…

We give an algorithm for computing the irreducible admissible representations of a real reductive group with regular integral infinitesimal character. This algorithm has been implemented on a computer, as part of the Atlas of Lie Groups and…

We classify finite groups $G$, such that the group algebra, $\mathbb{Q}G$ (over the field of rational numbers $\mathbb{Q}$), is the direct product of the group algebra $\mathbb{Q}[G/N]$ of a proper factor group $G/N$, and some division…

We state a conjecture on the reduction modulo the defining characteristic of a unipotent representation of a finite reductive group.

A primary covering of a finite group $G$ is a family of proper subgroups of $G$ whose union contains the set of elements of $G$ having order a prime power. We denote with $\sigma_0(G)$ the smallest size of a primary covering of $G$, and…

Let $G$ be a finite group and assume $p$ is a prime dividing the order of $G$. Suppose for any such $p$, that every two abelian $p$-subgroups of $G$ of equal order are conjugate. The structure of such a group $G$ has been settled in this…

A number is perfect if it is the sum of its proper divisors; here we call a finite group `perfect' if its order is the sum of the orders of its proper normal subgroups. (This conflicts with standard terminology but confusion should not…

We give a simple formula for the essential dimension of a finite pseudo-reflection group at a prime p and determine the absolute essential dimension for most irreducible pseudo-reflection groups. We also study the "poor man's essential…

This thesis studies arithmetic of linear algebraic groups. It involves studying the properties of linear algebraic groups defined over global fields, local fields and finite fields, or more generally the study of the linear algebraic groups…

This paper gives a complete classification of the finite groups that contain a strongly closed p-subgroup for p any prime.

We determine all the ways in which a direct product of two finite groups can be expressed as the set-theoretical union of proper subgroups in a family of minimal cardinality.

We study and classify a class of representations (called generalized geometric representations) of a Coxeter group of finite rank. These representations can be viewed as a natural generalization of the geometric representation. The…

This survey on the automorphism groups of finite p-groups focuses on three major topics: explicit computations for familiar finite p-groups, such as the extraspecial p-groups and Sylow p-subgroups of Chevalley groups; constructing p-groups…

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 prove that various classical conformal diffeomorphism groups, which are known to be essential [1], are in fact properly essential. This is a consequence of a local criterion on a conformal diffeomorphism in the form of a cohomological…