Related papers: Semitransitive and transitive subsemigroups of the…

A subsemigroup $S$ of an inverse semigroup $Q$ is a left I-order in $Q$, if every element in $Q$ can be written as $a^{-1}b$ where $a, b \in S$ and $a^{-1}$ is the inverse of $a$ in the sense of inverse semigroup theory. We study a…

We study varieties of semigroups related to completely 0-simple semigroup. We present here an algorithmic descriptions of these varieties interms of "forbidden" semigroups.

We describe and count the maximal subsemigroups of many well-known monoids of transformations and monoids of partitions. More precisely, we find the maximal subsemigroups of the full spectrum of monoids of order- or orientation-preserving…

In this paper, we characterize completely the structure of Clifford semigroups of matrices over an arbitrary field. It is shown that a semigroups of matrices of finite order is a Clifford semigroup if and only if it is isomorphic to a…

A subgroup $H$ of a finite group $G$ is submodular in $G$ if there is a subgroup chain $H=H_0\leq\ldots\leq H_i\leq H_{i+1}\leq \ldots \leq H_n=G$ such that $H_i$ is a modular subgroup of $H_{i+1}$ for every $i$. We investigate finite…

This report aims at giving a general overview on the classification of the maximal subgroups of compact Lie groups (not necessarily connected). In the first part, it is shown that these fall naturally into three types: (1) those of trivial…

This is an account of the theory of inverse semigroups, assuming only that the reader knows the basics of semigroup theory.

We study the so-called closed and splitting subsemimodules and submodules of a given semimodule or module, respectively. We describe lattices of subsemimodules and of closed subsemimodules and posets of splitting subsemimodules and…

The purpose of this paper is to study the generalization of inverse semigroups (without order). An ordered semigroup S is called an inverse ordered semigroup if for every a 2 S, any two inverses of a are H-related. We prove that an ordered…

Starting from the symmetric group $S_n$, we construct two fiat $2$-categories. One of them can be viewed as the fiat "extension" of the natural $2$-category associated with the symmetric inverse semigroup (considered as an ordered semigroup…

This work completes the classification of the imprimitive irreducible modules, over algebraically closed fields of characteristic 0, of the finite quasisimple groups.

Structures of commuting semigroups of isometries under certain additional assumptions like double commutativity or dual double commutativity are found.

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

We introduce and study the concept of cyclicity degree of a finite group $G$. This quantity measures the probability of a random subgroup of $G$ to be cyclic. Explicit formulas are obtained for some particular classes of finite groups. An…

Periodic and quasi-periodic orbits of the $n$-body problem are critical points of the action functional constrained to the Sobolev space of symmetric loops. Variational methods yield collisionless orbits provided the group of symmetries…

In this short note, we show that the number of monogenic submonoids of the full transformation monoid of degree $n$ for $n > 0$, equals the sum of the number of cyclic subgroups of the symmetric groups on $1$ to $n$ points. We also prove an…

In this paper we introduce and study the relative cyclic subgroup commutativity degrees of a finite group. We show that there is a finite group with $n$ such degrees for all $n \in \mathbb{N}^*\setminus \lbrace 2\rbrace$ and we indicate…

We investigate invertible matrices over finite additively idempotent semirings. The main result provides a criterion for the invertibility of such matrices. We also give a construction of the inverse matrix and a formula for the number of…

Here we introduce the notion of (left, right) $\pi$-$t$-simple, right $\pi$-inverse ordered semigroups and discuss characterizations and relationships concerning them. Semilattice decomposition of left $\pi$-$t$-simple ordered semigroups…

Crisp and lattice-valued ambiguous representations of one continuous semilattice in another one are introduced and operation of taking pseudo-inverse of the above relations is defined. It is shown that continuous semilattices and their…