Related papers: Codegrees of primitive characters of solvable grou…

This book describes some computational methods to deal with modular characters of finite groups. It is the theoretical background of the MOC system of the same authors. This system was, and is still used, to compute the modular character…

We give formulae relating the value of an irreducible character of a classical group at a matrix to entries of powers of the matrix. This yields a far-reaching generalization of a result of J. L. Cisneros-Molina concerning the $GL_2$ case.

We compute the number of points over finite fields of the character stack associated to a compact surface group and a reductive group with connected centre. We find that the answer is a Polynomial On Residue Classes (PORC). The key…

We verify a finiteness conjecture of Feit on sources of simple modules over group algebras for various classes of finite groups related to the symmetric groups.

This note generalizes the Fibonacci primitive roots to the set of integers. An asymptotic formula for counting the number of integers with such primitive root is introduced here.

Building upon the author's previous work on primitivity testing of finite nilpotent linear groups over fields of characteristic zero, we describe precisely those finite nilpotent groups which arise as primitive linear groups over a given…

A new conjecture on characters of finite groups, related to the McKay conjecture, was proposed recently by the first and third authors. In this paper, we prove it for $p$-solvable groups when $p$ is odd.

Serre obtained a sharp bound on how often two irreducible degree $n$ complex characters of a finite group can agree, which tells us how many local factors determine an Artin $L$-function. We consider the more delicate question of finding a…

Let G be a finite non-abelian simple group and let p be a prime. We classify all pairs (G,p) such that the sum of the complex irreducible character degrees of G is greater than the index of a Sylow p-subgroup of G. Our classification…

We determine the fields of values of the Isaacs' head characters of a finite solvable group.

We construct a finitely presented (two-sided) totally orderable group with insoluble word problem.

We give a complete characterization of countable primitive groups in several settings including linear groups, subgroups of mapping class groups, groups acting minimally on trees and convergence groups. The latter category includes as a…

For polynomials of degree two over finite fields, we present an improvement of Fitzgerald's characterization (Finite Fields Appl. 9(1):117-121, 2003). We then use this new characterization to obtain an explicit, complete, and simple…

We study the primitive recursive analogue of computable categoricity spectra for various natural classes of structures. We show that these notions coincide for all relatively $\Delta_{2}^{0}$-categorical equivalence structures and linear…

The group generated by the round functions of a block ciphers is a widely investigated problem. We identify a large class of block ciphers for which such group is easily guaranteed to be primitive. Our class includes the AES and the…

We compare some algebras appeared in the recent attempts to prove resolution of singularities in positive characteristic. We also construct an algebra which encodes the same information and it is equivalent, up to integral closure, to the…

For a fixed integer $t \geq 2$, we consider the irreducible characters of representations of the classical groups of types A, B, C and D, namely $\text{GL}_{tn}, \text{SO}_{2tn+1}, \text{Sp}_{2tn}$ and $\text{O}_{2tn}$, evaluated at…

Computations of Miller and Scheinerman suggest that the vast majority of the zeros appearing in the character table of the symmetric group are of a certain special type. While we cannot prove this, we resolve a conjecture arising in their…

We find some general lower bounds of the sum of certain families of multigraded Betti numbers of any simplicial complex with a vertex coloring.

The concept of descent algebras over a field of characteristic zero is extended to define descent algebras over a field of prime characteristic. Some basic algebraic structure of the latter, including its radical and irreducible modules, is…