Related papers: Generalization of Frobenius' theorem for group det…

We construct irreducible unitary representations of a finitely generated free group which are weakly contained in the left regular representation and in which a given linear combination of the generators has an eigenvalue. When the…

We construct an infinite family of representations of finite groups with an irreducible adjoint action and we give an application to the question of lacunary of Frobenius traces in Galois representations.

This paper provides a realization of all classical and most exceptional finite groups of Lie type as Galois groups over function fields over F_q and derives explicit additive polynomials for the extensions. Our unified approach is based on…

Given a subgroup H of a finite group G, we begin a systematic study of the partial representations of G that restrict to global representations of H. After adapting several results from [DEP00] (which correspond to the case where H is…

Let $R$ be a standard graded finitely generated algebra over an $F$-finite field of prime characteristic, localized at its maximal homogeneous ideal. In this note, we prove that that Frobenius complexity of $R$ is finite. Moreover, we…

The Frobenius method can be used to compute solutions of ordinary linear differential equations by generalized power series. Each series converges in a circle which at least extends to the nearest singular point; hence exponentially fast…

The dominant theme of this thesis is the construction of matrix representations of finite solvable groups using a suitable system of generators. For a finite solvable group $G$ of order $N = p_{1}p_{2}\dots p_{n}$, where $p_{i}$'s are…

We prove a factorization theorem for Fuchsian groups similar to those proved by Agol and Liu for 3-manifold groups. As an application, we build Makanin-Razborov diagrams, which parametrize the collection of all discrete representations from…

We generalize the concept of a number derivative, and examine one particular instance of a deformed number derivative for finite field elements. We find that the derivative is linear when the deformation is a Frobenius map and go on to…

We prove the theorems which are equivalent to the Roland's results such that a new form of them allows to consider some generalizations. In particular, we give generators of primes more than a fixed prime.

We give parameterizations of the irreducible representations of finite groups of Lie type in their defining characteristic.

We introduce a weighted sum of irreducible character ratios as an estimator for commutator probabilities. The estimator yields Frobenius formula when applied to a regular representation

We show that the universal theory of torsion groups is strongly contained in the universal theory of finite groups. This answers a question of Dyson. We also prove that the universal theory of some natural classes of torsion groups is…

We reformulate the statement of the Feit-Thompson theorem in terms of diagrams in the category of finite groups, namely iterations of the Quillen lifting property with respect to particular morphisms.

We describe the construction which takes as input a profinite group, which when applied the the absolute Galois group of a geometric field F agrees in some cases with the algebraic K-theory of F. We prove that it agrees in the case of a…

We prove a generalized Fej\'er's theorem for locally compact groups.

The authors show that a wide class of Fredholm determinants arising in the representation theory of "big" groups such as the infinite-dimensional unitary group, solve Painleve equations. Their methods are based on the theory of integrable…

For a finite group $G$, Frobenius found a formula for the values of the function $\sum_{\mathrm{Irr} G} (\dim\, \pi)^{-s}$ for even integers $s$, where $\mathrm{Irr} G$ is the set of irreducible representations of $G$. We generalize this…

Lewis, Reiner, and Stanton conjectured a Hilbert seriesfor a space of invariants under an action of finite general linear groups using $(q,t)$-binomial coefficients. This work gives an analog in positive characteristic of theorems relating…

We define basic notions in the category of conic representations of a topological group and prove elementary facts about them. We show that a conic representation determines an ordinary dynamical system of the group together with a…