Related papers: Advertising finite commutative semigroups

The aim of this paper is to present the main constructions of the substructures of an almost groupoid and to discuss their basic properties. The definitions and properties concerning these new algebraic constructions extend to almost…

Universality of quantum mechanics -- its applicability to physical systems of quite different nature and scales -- indicates that quantum behavior can be a manifestation of general mathematical properties of systems containing…

This article determines the structure of the group ring $\mathbb{Z}_nG$, where $G$ is a finite group and $\mathbb{Z}_n$ is the ring of integers modulo $n$, such that $n$ is relatively prime to the order of $G$. The decomposition of…

Primitive representations of finite groups as well as primitive finite groups were classified in the O'Nan-Scott Theorem. In this paper we classify faithful finite primitive semigroup representations. To each finite primitive…

We give extensions of results on nonnegative matrix semigroups which deduce finiteness or boundedness of such semigroups from the corresponding local properties, e.g., from finiteness or boundedness of values of certain linear functionals…

We study the structure of nilpotent subsemigroups in the semigroup $M(n,\mathbb{F})$ of all $n\times n$ matrices over a field, $\mathbb{F}$, with respect to the operation of the usual matrix multiplication. We describe the maximal…

This paper has several purposes. We present through a critical review the results from already published papers on the constructive semigroup theory, and contribute to its further development by giving solutions to open problems. We also…

In this note we study the finite groups whose subgroup lattices are dismantlable.

The representation theory of finite groups began with Frobenius's factorization of Dedekind's group determinant. In this paper, we consider the case of the semigroup determinant. The semigroup determinant is nonzero if and only if the…

A finite group $G$ is called uniformly semi-rational if there exists an integer $r$ such that the generators of every cyclic sugroup $\langle x \rangle$ of $G$ lie in at most two conjugacy classes, namely $x^G$ or $(x^r)^G$. In this paper,…

We give a classification of all quasitriangular structures and ribbon elements of $\mathcal{D}(G)$ explicitly in terms of group homomorphisms and central subgroups. This can equivalently be interpreted as an explicit description of all…

We deduce a simple representation and the invariant factor decompositions of the subgroups of the group $\Bbb{Z}_m \times \Bbb{Z}_n$, where $m$ and $n$ are arbitrary positive integers. We obtain formulas for the total number of subgroups…

We determine all finite subgroups of simple algebraic groups that have irreducible centralizers - that is, centralizers whose connected component does not lie in a parabolic subgroup.

Working in a theory with an integer-valued dimension on interpretable sets, we classify pseudofinite definably primitive permutation groups acting on one-dimensional sets which satisfy a version of chain condition on centralizers and on…

This work delves into the {\it quotient of an affine semigroup by a positive integer}, exploring its intricate properties and broader implications. We unveil an {\it associated tree} that serves as a valuable tool for further analysis.…

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 prove the definability, and actually the finiteness of the commutator width, of many commutator subgroups in groups definable in o-minimal structures. It applies in particular to derived series and to lower central series of solvable…

We develop a structure theory of connected solvable spherical subgroups in semisimple algebraic groups. Based on this theory, we obtain an explicit classification of all such subgroups up to conjugation.

We describe the structure of finite groups with $\mathfrak{F}$-subnormal or self-normalizing primary cyclic subgroups when $\mathfrak{F}$ is a subgroup-closed saturate superradical formation containing all nilpotent groups. We prove that…

We study finite groups which possess a strongly p-embedded subgroup for some odd prime p. The main results of the paper will be applied in the ongoing project to classify the simple groups of local characteristic p.