Related papers: Finite Decomposition Semigroups

This paper gives a systematic construction of certain covers of finite semigroups. These covers will be used in future work on the complexity of finite semigroups.

Every mathematician is familiar with the beautiful structure of finite commutative groups. What is less well known is that finite commutative semigroups also have a neat and well-described structure. We prove this in an efficient fashion.…

The structure of groups for which certain sets of commutator subgroups are finite is investigated, with a particular focus on the relationship between these groups and those with finite derived subgroup.

Necessary and sufficient conditions for finite semihypergroups to be built from groups of the same order are established

The goal of this paper is to provide some basic structure information on derivations in finite semirings.

We describe the structure of finite Boolean inverse monoids and apply our results to the representation theory of finite inverse semigroups. We then generalize to semisimple Boolean inverse semigroups.

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…

In this article we introduce and study a class of finite groups for which the orders of normal subgroups satisfy a certain inequality. It is closely connected to some well-known arithmetic classes of natural numbers.

In this paper, the complete algebraic structure of finite semisimple group algebra of a normally monomial group is described. The main result is illustrated by computing the explicit Wedderburn decomposition of finite semisimple group…

This is a survey, intended both for group theorists and model theorists, concerning the structure of pseudofinite groups, that is, infinite models of the first order theory of finite groups. The focus is on concepts from stability theory…

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

Suppose that $G$ is a finite group and $H$ is a subgroup of $G$. We say that $H$ is s-semipermutable in $G$ if $HG_p = G_pH$ for any Sylow $p$-subgroup $G_p$ of $G$ with $(p, |H|) = 1$. We investigate the influence of s-semipermutable…

A survey of recent results about profinite groups, and results about infinite and finite groups where the theory of profinite groups plays a leading role.

This document gives a list of finite semigroups that are interesting from the point of view of Krohn-Rhodes complexity theory. The list will be expanded and updates as "time goes by".

We develop the representation theory of a finite semigroup over an arbitrary commutative semiring with unit, in particular classifying the irreducible and minimal representations. The results for an arbitrary semiring are as good as the…

Necessary and sufficient conditions for finite commutative semihypergroups to be built from abelian groups of the same order are established.

Every semigroup which is a finite disjoint union of copies of the free monogenic semigroup (natural numbers under addition) is finitely presented and residually finite.

We describe all finite subsemigroups of a free left regular band of infinite rank. Moreover, we show applications of this result in algebraic geometry and model theory.

In this paper we introduce the notion of m-irreducibility that extends the standard concept of irreducibility of a numerical semigroup when the multiplicity is fixed. We analyze the structure of the set of m-irreducible numerical…

In this paper we show that if $Y$ is a subsemilattice of a finite semilattice indecomposable semigroup $S$ then $|Y|\leq 2\left\lfloor \frac{|S|-1}{4}\right\rfloor+1$. We also characterize finite semilattice indecomposable semigroups $S$…