Related papers: Some results in constructive semigroup theory

First we identify the free algebras of the class of algebras of binary relations equipped with the composition and domain operations. Elements of the free algebras are pointed labelled finite rooted trees. Then we extend to the analogous…

Motivated by recent appearance of multivalued structures in categorification, tropical geometry and other areas, we study basic properties of abstract multisemigroups. We give many new and old examples and general constructions for…

We develop a semigroup-theoretic analogue of liaison for relative ideals of a numerical semigroup. Two parallel linkage notions are proposed: a theory based on translates of the semigroup and a theory based on translates of the canonical…

In this paper we elaborate on the structure of the semigroup tree and the regularities on the number of descendants of each node observed earlier. These regularites admit two different types of behavior and in this work we investigate which…

For an arbitrary rational polyhedron we consider its decompositions into Minkowski summands and, dual to this, the free extensions of the associated pair of semigroups. Being free for the pair of semigroups is equivalent to flatness for the…

When a semigroup has a unary operation, it is possible to define two binary operations, namely, left and right division. In addition it is well known that groups can be defined in terms of those two divisions. The aim of this paper is to…

We prove that the structure of right generalized inverse semigroups is determined by free \'etale actions of inverse semigroups. This leads to a tensor product interpretation of Yamada's classical struture theorem for generalized inverse…

Every semigroup which is a finite disjoint union of copies of the free mono- genic semigroup (natural numbers under addition) has soluble word prob- lem and soluble membership problem. Efficient algorithms are given for both problems.

We define a class of finite groups based on the properties of the closed twins of their power graphs and study the structure of those groups. As a byproduct, we obtain results about finite groups admitting a partition by cyclic subgroups.

This is an exposition of homotopical results on the geometric realization of semi-simplicial spaces. We then use these to derive basic foundational results about classifying spaces of topological categories, possibly without units. The…

We use semigroup theory to describe the group of automorphisms of some semigroups of interest in holomorphic dynamical systems. We show, with some examples, that representation theory of semigroups is related to usual constructions in…

A quasi-automatic semigroup is defined by a finite set of generators, a rational (regular) set of representatives, such that if a is a generator or neutral, then the graph of right multiplication by a on the set of representatives is a…

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.

The structure of categorical at zero semigroups is studied from the point of view their likeness to categories.

Building on the previous extensive study of Yang, Gould and the present author, we provide a more precise insight into the group-theoretical ramifications of the word problem for free idempotent generated semigroups over finite biordered…

We report on recent progress concerning the relationship that exists between the algebraic structure of a finite group and certain features of its class-size prime graph.

Combinatorial objects such as rooted trees that carry a recursive structure have found important applications recently in both mathematics and physics. We put such structures in an algebraic framework of operated semigroups. This framework…

We present a study of semigroup compactifications of a semitopological semigroup $S$ using certain filters on $S$. We characterize closed subsemigroups and closed left, right, and two-sided ideals in any semigroup compactification of any…

In this paper we first survey some basic results in the cohomology of finite groups, and then discuss recent work on constructing free actions of finite groups on products of spheres.

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