Related papers: On generators of arithmetic groups over function f…

Let $Q$ be the matrix $\displaystyle \begin{pmatrix} a & b \\ 1 & 0 \end{pmatrix}$ in $GL_2(\mathbb{F}_q)$ where $\mathbb{F}_q$ is a finite field, and let $G$ be the finite cyclic group generated by $Q$. We consider the action of $G$ on the…

We prove an analog of the Tits alternative for rational functions. In particular, we show that if $S$ is a finitely generated semigroup of rational functions over the complex numbers, then either $S$ has polynomially bounded growth or $S$…

Let $D$ be a division ring with center $F$, $f(x_1,x_2,\dots, x_m)$ a non-central multilinear polynomial over $F$, and $w(x_1,x_2,\dots,x_m)$ a non-trivial word. In this paper, we investigate conditions under which there exists an element…

Given a finitely generated subgroup G of a ring R we provide a finite subset of G such that if each element of this set satisfies some cubic polynomial equation in one variable over the center Z of R then the subring generated by G has…

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…

Let $L$ be the language of rings. We provide an axiomatization of the $L$-theories of quaternions and octonions and characterize their models: they coincide, up to isomorphism, with quaternion and octonion algebras over a real closed field,…

Let $\mathbb F_q$ be the finite field with $q$ elements, where $q$ is a power of a prime. We discuss recursive methods for constructing irreducible polynomials over $\mathbb F_q$ of high degree using rational transformations. In particular,…

Let $C_n$, $Q_n$ and $D_n$ be the cyclic group, the quaternion group and the dihedral group of order $n$, respectively. The structures of the unit groups of the finite group algebras $FQ_{12}$ and $F(C_2 \times Q_{12})$ over a finite field…

Heisenberg groups over algebras with central involution and their automorphism groups are constructed. The complex quaternion group algebra over a prime field is used as an example. Its subspaces provide finite models for each of the real…

Let $\mathbb{F}_{q}$ be the finite field with $q$ elements. This paper mainly researches the polynomial representation of double cyclic codes over $\mathbb{F}_{q}+v\mathbb{F}_{q}+v^2\mathbb{F}_{q}$ with $v^3=v$. Firstly, we give the…

We make a list of finite simple groups whose group rings over a given field are serial.

We determine when an arithmetic subgroup of a reductive group defined over a global function field is of type FP_\infty by comparing its large-scale geometry to the large-scale geometry of lattices in real semisimple Lie groups.

Fibonacci polynomials are generalizations of Fibonacci numbers, so it is natural to consider polynomial versions of the various results for Fibonacci numbers. According to Hong, Pongsriiam, Bulawa, and Lee, the generating function of the…

The notion of symmetry in polynomial rings with several indeterminates is generalized to polynomial rings over finite fields. Families of extensions of the projective line over a finite field of constants possessing this property are…

Let $R$ be a complete regular local ring with an algebraically closed residue field and let $A$ be a Noetherian $R$-subalgebra of the polynomial ring $R[X]$. It has been shown in \cite{DO2} that if $\dim R=1$, then $A$ is necessarily…

We prove a new formula for the generating function of polynomials counting absolutely stable representations of quivers over finite fields. The case of irreducible representations is studied in more detail.

Let G be a connected, semisimple Lie group with finite center and let K be a maximal compact subgroup. We investigate a method to compute multiplicities of K-types in the discrete series using a rational expression for a generating function…

Let E be a number field and G be a finite group. Let A be any O_E-order of full rank in the group algebra E[G] and X be a (left) A-lattice. We give a necessary and sufficient condition for X to be free of given rank d over A. In the case…

Rational transformations of polynomials are extensively studied in the context of finite fields, especially for the construction of irreducible polynomials. In this paper, we consider the factorization of rational transformations with…

In this paper we compute extension groups in the category of strict polynomial superfunctors and thereby exhibit certain "universal extension classes" for the general linear supergroup. Some of these classes restrict to the universal…