Related papers: Factorizations of almost simple unitary groups

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 finite group $G$ is called $k$-factorizable if for every ordered factorization $|G|=a_1\cdots a_k$ into integers each greater than $1$ there exist subsets $A_1,\dots,A_k\subseteq G$ such that $|A_i|=a_i$ for each $i$ and $G=A_1\cdots…

Every numerical semigroup can be expressed as an intersection of irreducible numerical semigroups. We show that the unions of sets of lengths of factorizations of numerical semigroups into irreducible numerical semigroups are all equal to…

In this paper, we classify the finite simple groups with an abelian Sylow subgroup.

We initiate the study of $\lambda$-fold near-factorizations of groups with $\lambda > 1$. While $\lambda$-fold near-factorizations of groups with $\lambda = 1$ have been studied in numerous papers, this is the first detailed treatment for…

This expository article revolves around the question to find short presentations of finite simple groups. This subject is one of the most active research areas of group theory in recent times. We bring together several known results on…

Let $G$ be a finite group and let $A_1,\ldots,A_k$ be a collection of subsets of $G$ such that $G=A_1\ldots A_k$ is the product of all the $A_i$'s with $|G|=|A_1|\ldots|A_k|$. We write $G=A_1\cdot\ldots\cdot A_k$ and call this a $k$-fold…

In this paper, we continue the study of almost squares and extend the result of the author's fourth paper of the series to almost squares with closer factors.

In this article, we study short intervals that contain another type of "almost square", an integer $n$ which can be factored in two different ways $n = a_1 b_1 = a_2 b_2$ with $a_1, a_2, b_1, b_2$ close to $\sqrt{n}$.

We factorize harmonic maps with values in a semisimple Lie groups in a product of harmonic maps with values in the components of the Iwasawa decomposition. In particular, we use this factorization to study the harmonic maps from…

Often a localization functor (in the category of groups) sends a finite simple group to another finite simple group. We study when such a localization also induces a localization between the automorphism groups and between the universal…

We have classified, upto isoclinism, certain groups with a given central factor. As an application, we classify, upto isoclinism, groups having at the most nine element centralizers. Among other results of independent interest, we have…

We investigate classifications of quasitrivial semigroups defined by certain equivalence relations. The subclass of quasitrivial semigroups that preserve a given total ordering is also investigated. In the special case of finite semigroups,…

In our previous paper, we gave a complete list of the finite non-abelian simple groups whose holomorph contains a solvable regular subgroup. In this paper, we refine our previous work by considering all finite almost simple groups. In…

In this paper, we introduce a kind of decomposition of a finite group called a uniform group factorization, as a generalization of exact factorizations of a finite group. A group $G$ is said to admit a uniform group factorization if there…

This note deals with the computation of the factorization number $F_2(G)$ of a finite group $G$. By using the M\"{o}bius inversion formula, explicit expressions of $F_2(G)$ are obtained for two classes of finite abelian groups, improving…

We investigate simple endotrivial modules of finite quasi-simple groups and classify them in several important cases. This is motivated by a recent result of Robinson showing that simple endotrivial modules of most groups come from…

A group $G$ is said to be factorized into subsets $A_1, A_2, \ldots, A_s\subseteq G$ if every element $g$ in $G$ can be uniquely represented as $g=g_1g_2\ldots g_s$, where $g_i\in A_i$, $i=1,2,\ldots,s$. We consider the following…

Noncommutative near-group fusion categories were completely classified in the previous work of the first named author by using an operator algebraic method (and hence under the assumption of unitarity), and they were shown to be group…

We introduce the concept of isolated factorizations of an element of a commutative monoid and study its properties. We give several bounds for the number of isolated factorizations of simplicial affine semigroups and numerical semigroups.…