Related papers: The normal subgroup structure of ZM-groups
The goal of this note is to give a characterization of generalized quaternion $2$-groups by using their posets of cyclic subgroups.
Let $G$ be a finite group and $N$ a normal subgroup of $G$. We determine the structure of $N$ when the diameter of the graph associated to the $G$-conjugacy classes contained in $N$ is as large as possible, that is, is equal to three.
We generalize the idea of a Schur ring of a group to the category of semigroups. Fundamental results of Schur rings over groups are shown to be true for Schur rings over semigroups. Examples where Schur rings differ between the two…
We consider finite groups having a conjugacy class that is the difference of two normal subgroups. That is, suppose $G$ is a group and $M$ and $N$ are normal subgroups so that $N < M$, and suppose that there is an element $g \in G$ so that…
Finite hamiltonian groups are counted. The sequence of numbers of all groups of order $n$ all whose subgroups are normal and the sequence of numbers of all groups of order less or equal to $n$ all whose subgroups are normal are presented.
A subgroup $H$ of a finite group $G$ is said to be an $\mathscr{H}C$-subgroup of $G$ if there exists a normal subgroup $T$ of $G$ such that $G=HT$ and $H^g \cap N_T(H)\leq H$ for all $g\in G$. In this paper, we investigate the structure of…
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…
A characterization of congruences in free semigroups is presented.
This survey aims to give an overview of several substantial developments of the last 50 years in the structure theory of regular semigroups and to shed light on their impact on other parts of semigroup theory.
The aim of this article is to draw attention towards various natural but unanswered questions related to the lower central series of the unit group of an integral group ring.
In this short note we give a formula for the number of chains of subgroups of a finite elementary abelian $p$-group. This completes our previous work [5].
We establish a necessary and sufficient condition for a normal subgroup of a finite group to be a subgroup perfect code.
We investigate the maximum length of a chain of subsemigroups in various classes of semigroups, such as the full transformation semigroups, the general linear semigroups, and the semigroups of order-preserving transformations of finite…
We investigate the class $\mathcal{MN}$ of groups with the property that all maximal subgroups are normal. The class $\mathcal{MN}$ appeared in the framework of the study of potential counter-examples to the Andrews-Curtis conjecture. In…
We introduce the notion of pattern for numerical semigroups, which allows us to generalize the definition of Arf numerical semigroups. In this way infinitely many other classes of numerical semigroups are defined giving a classification of…
A subgroup of a group is contranormal if its normal closure coincides with the group. We call such groups without proper contranormal subgroups contranormal-free. In this paper we prove various results concerning contranormal-free groups…
Consideration of certain properties of group rings and their ideals search
Let $X$ be a finite set such that $|X|=n$. Let $\trans$ and $\sym$ denote respectively the transformation monoid and the symmetric group on $n$ points. Given $a\in \trans\setminus \sym$, we say that a group $G\leq \sym$ is $a$-normalizing…
The main purpose of this paper is to introduce the structure of soft group category. In this category, we determine some special objects and morphisms having a universal structure such as the final object and product. Therefore, the…
The spectrum of a finite group is the set of element orders of this group. The main goal of this paper is to survey results concerning recognition of finite simple groups by spectrum, in particular, to list all finite simple groups for…