Related papers: Constructing solvable groups with derived length f…
Let $G$ be a finite solvable group and $\chi, \psi \in \Irr(G)$ be complex characters of $G$. Let $\alpha$ be an irreducible constituent of the product $\chi \psi$. We show that the derived length of $\Ker(\alpha)/\Ker(\chi\psi)$ is bounded…
We study the degree of the special cubic fourfolds in the Hilbert scheme of cubic fourfolds via a computation of the generating series of Heegner divisors of even lattice of signature (2, 20).
This paper focuses on the derivations and automorphism groups of certain finite-dimensional associative algebras over the field of complex numbers. Using classification results for algebras of dimensions two, three, and four, along with…
In this paper we investigate families of connected graphs which do not contain an odd cycle in their complement. Specifically, we consider graphs formed by two complete graphs connected in a particular way. We determine which of these…
We present the solutions of equations of degrees 3 and 4 using Galois theory and some simple Fourier analysis for finite groups, together with historical comments on these and other solution methods.
The paper studies constructions of irreducible polynomials over finite fields using polynomial composition method.
In this paper, we prove a series of results on group embeddings in groups with a small number of generators. We show that each finitely generated group $G$ lying in a variety ${\mathcal M}$ can be embedded in a $4$-generated group $H \in…
Group cohomology of polynomial growth is defined for any finitely generated discrete group, using cochains that have polynomial growth with respect to the word length function. We give a geometric condition that guarantees that it agrees…
We describe general methods for enumerating subsemigroups of finite semigroups and techniques to improve the algorithmic efficiency of the calculations. As a particular application we use our algorithms to enumerate all transformation…
Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider…
We construct an explicit family of modular iterated integrals which involves cusp forms. This leads to a new method of producing "invariant versions" of iterated integrals of modular forms. The construction will be based on an extension of…
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 study systematically groups whose marked finite quotients form a recursive set. We give several definitions, and prove basic properties of this class of groups, and in particular emphasize the link between the growth of the depth…
Several recently discovered properties of multiple families of special polynomials (some orthogonal and some not) that satisfy certain differential, difference or q-difference equations are reviewed. A general method of construction of…
The solvable Farb growth of a group quantifies how well-approximated the group is by its finite solvable quotients. In this note we present a new characterization of polycyclic groups which are virtually nilpotent. That is, we show that a…
Cyclic codes are an interesting subclass of linear codes and have been used in consumer electronics, data transmission technologies, broadcast systems, and computer applications due to their efficient encoding and decoding algorithms. In…
We propose a novel approach for studying rooted trees by using functions that we will call descent functions. We provide a construction method for rooted trees that allows to study their properties through the use of descent functions.…
We construct a finitely generated solvable subgroup of Homeo(R) with a non-metaabelian characterizing quotient.
MDS self-dual codes have nice algebraic structures and are uniquely determined by lengths. Recently, the construction of MDS self-dual codes of new lengths has become an important and hot issue in coding theory. In this paper, we develop…
We characterize the finite groups of minimal order that admit an irreducible complex character of degree $p$ or $p^2$, where $p$ is a prime.