Related papers: Reaching the minimum ideal in a finite semigroup

Various descending chains of subgroups of a finite permutation group can be used to define a sequence of `basic' permutation groups that are analogues of composition factors for abstract finite groups. Primitive groups have been the…

By using the structure and some properties of extraspecial and generalized/almost extraspecial $p$-groups, we explicitly determine the number of elements of specific orders in such groups. As a consequence, one may find the number of cyclic…

In a recent paper Cameron, Lakshmanan and Ajith began an exploration of hypergraphs defined on algebraic structures, especially groups, to investigate whether this can add a new perspective. Following their suggestions, we consider suitable…

We investigate the intersection problem for finite semigroups, which asks for a given set of regular languages, represented by recognizing morphisms to finite semigroups, whether there exists a word contained in their intersection. We…

We improve the upper bounds (in terms of $n$) in [9] and [13] on the minimal number of elements required to generate a minimally transitive permutation group of degree $n$.

We propose a notion of a proper Ehresmann semigroup based on a three-coordinate description of its generating elements governed by certain labelled directed graphs with additional structure. The generating elements are determined by their…

This paper deals with a simple and straightforward procedure for automatic generation of finite-element or finite-volume meshes of spheroidal domains, consisting of tetrahedra. Besides the equation of the boundary, the generated meshes…

In this paper we study the regular semigroups weakly generated by a single element x, that is, with no proper regular subsemigroup containing x. We show there exists a regular semigroup $F_1$ weakly generated by x such that all other…

The question of computing the group complexity of finite semigroups and automata was first posed in K. Krohn and J. Rhodes, \textit{Complexity of finite semigroups}, Annals of Mathematics (2) \textbf{88} (1968), 128--160, motivated by the…

The thesis is devoted to abstract, geometric and symmetric aspects of modern elementary particle theories. A new direction in constructing supersymmetric and superstring models based on consequent and strong consideration and inclusion of…

This article introduces patterns of ideals of numerical semigroups, thereby unifying previous definitions of patterns of numerical semigroups. Several results of general interest are proved. More precisely, this article presents results on…

A generalized numerical semigroup is a submonoid $S$ of $\mathbb{N}^d$ with finite complement in it. We characterize isomorphisms between these monoids in terms of permutation of coordinates. Considering the equivalence relation that…

We construct minimal and irredundant generating sets for a family of submonoids of the monoid of $n \times n$ upper triangular matrices over a commutative semiring. We show that the monoid of $n \times n$ matrices over the tropical…

In this paper, we study the class of affine semigroup generated by integral vectors, whose components are in generalised arithmetic progression and we observe that the defining ideal is determinantal. We also give a sufficient condition on…

We introduce the concept of boundariness capturing the most efficient way of expressing a given element of a convex set as a probability mixture of its boundary elements. In other words, this number measures (without the need of any…

We define the class of multivariate group entropies as a novel set of information - theoretical measures, which extends significantly the family of group entropies. We propose new examples related to the "super-exponential" universality…

We augment the body of existing results on embedding finite semigroups of a certain type into 2-generator finite semigroups of the same type. The approach adopted applies to finite semigroups the idempotents of which form a band and also to…

This work establishes a new probabilistic bound on the number of elements to generate finite nilpotent groups. Let $\varphi_k(G)$ denote the probability that $k$ random elements generate a finite nilpotent group $G$. For any $0 < \epsilon <…

We construct a family of finitely generated infinite periodic groups. The basic example is a 2-group, called the tetrahedron group. We generalize the construction by suggesting a family of infinite finitely generated dice groups. We provide…

An unrefinable chain of a finite group $G$ is a chain of subgroups $G = G_0 > G_1 > \cdots > G_t = 1$, where each $G_i$ is a maximal subgroup of $G_{i-1}$. The length (respectively, depth) of $G$ is the maximal (respectively, minimal)…