Related papers: Consonant inverse semigroups

Given an adaptable separated graph, we construct an associated groupoid and explore its type semigroup. Specifically, we first attach to each adaptable separated graph a corresponding semigroup, which we prove is an $E^*$-unitary inverse…

Let $P,$ $S,$ and $T$ be semigroups, $f:P\to S$ and $g:P\to T$ semigroup homomorphisms, and $X$ a generating set for $S$ (possibly infinite). Clearly, a <i>necessary</i> condition for there to exist a homomorphism $S\to T$ making a…

We systematically develop a theory of graded semigroups, that is semigroups S partitioned by groups G, in a manner compatible with the multiplication on S. We define a smash product S#G, and show that when S has local units, the category…

This note proves a generalisation to inverse semigroups of Anisimov's theorem that a group has regular word problem if and only if it is finite, answering a question of Stuart Margolis. The notion of word problem used is the two-tape word…

We study translationally-invariant insulators with inversion symmetry that fall outside the established classification of topological insulators. These insulators are not required to have gapless boundary modes in the energy spectrum.…

Two finite groups $L_1$ and $L_2$ are compatible if there exists a finite group $G$ with isomorphic normal subgroups $N_1$ and $N_2$ such that $L_1\cong G/N_1$ and $L_2\cong G/N_2$. We prove a new sufficient condition for two groups to be…

A DR-semigroup $S$ (also known as a reduced E-semiabundant or reduced E-Fountain semigroup) is here viewed as a semigroup equipped with two unary operations $D,R$ satisfying finitely many equational laws. Examples include DRC-semigroups…

An inverse monoid $S$ is called $F$-inverse if each $\sigma$-class of $S$, where $\sigma$ is the minimum group congruence of $S$, has a maximum element with respect to the natural order of $S$. Since the property of an inverse monoid being…

Let $S_\infty$ denote the topological group of permutations of the natural numbers. We study the complexity of the isomorphism relation on classes of closed subgroups $S_\infty$ in the setting of Borel reducibility between equivalence…

It was proved by Oliveira and Silva (2005) that every finitely generated inverse subsemigroup of the monogenic free inverse semigroup $FI_1$ is finitely presented. The present paper continues this development, and gives generating sets and…

We build a combinatorial invariant, called the spectral monodromy from the spectrum of a non-selfadjoint h -pseudodifferential operator with two degrees of freedom in the semi-classical limit. We treat small non-selfadjoint perturbation of…

We give a method of constructing maps between tubular groups inductively according to a set of strategies. This map will be a quasi-isometry exactly when the set of strategies is consistent. Conversely, if there exists a quasi-isometry…

We describe the structure of Hausdorff locally compact semitopological $0$-bisimple inverse $\omega$-semigroups with compact maximal subgroups. In particular, we show that a Hausdorff locally compact semitopological $0$-bisimple inverse…

Given an action $\varphi$ of of inverse semigroup $S$ on a ring $A$ (with domain of $\varphi(s)$ denoted by $D_{s^*}$) we show that if the ideals $D_e$, with $e$ an idempotent, are unital, then the skew inverse semigroup ring $A\rtimes S$…

For a topological monoid S the dual inverse monoid is the topological monoid of all identity preserving homomorphisms from S to the circle with attached zero. A topological monoid S is defined to be reflexive if the canonical homomorphism…

In this paper we investigate graph inverse semigroups which are subsemigroups of compact-like topological semigroups. More precisely, we characterise graph inverse semigroups which admit a compact semigroup topology and describe graph…

We show that \'etale correspondences between ample groupoids induce homomorphisms of homology groups. To complement this we explore the module categories of ample groupoids. We construct an induction-restriction adjunction for subgroupoids,…

The index of a subgroup of a group counts the number of cosets of that subgroup. A subgroup of finite index often shares structural properties with the group, and the existence of a subgroup of finite index with some particular property can…

Let $(G,*)$ and $(G',\cdot)$ be groupoids. A bijection $f: G \rightarrow G'$ is called a half-isomorphism if $f(x*y)\in\{f(x)\cdot f(y),f(y)\cdot f(x)\}$, for any $ x, y \in G$. A half-isomorphism of a groupoid onto itself is a…

We present a construction for the holomorph of an inverse semigroup, derived from the cartesian closed structure of the category of ordered groupoids. We compare the holomorph with the monoid of mappings that preserve the ternary heap…