Related papers: Gcd-monoids arising from homotopy groupoids

In this paper we show that polycyclic monoids are universal objects in the class of graph inverse semigroups. In particular, we prove that a graph inverse semigroup $G(E)$ over a directed graph $E$ embeds into the polycyclic monoid…

In this paper, we extend the classical theory of crossed $G$-sets and the crossed Burnside ring from a finite group $G$ to a finite groupoid $\mathcal{G}$. We introduce a natural monoidal structure on the category of crossed…

Fix a prime $p$ and an integer $m$ with $p> m \geq 2$. Define the family of finite groups \[ G_n :=SL_m (\mathbb{Z}/p^{n}\mathbb{Z}) \] for $n=1,2,... $. We will prove that there exist two positive constants $C$ and $d$ such that for any…

Let p be a prime. Uniform pro-p groups play a central role in the theory of p-adic Lie groups. Indeed, a topological group admits the structure of a p-adic Lie group if and only if it contains an open pro-p subgroup which is uniform.…

In this paper, we prove a series of results on group embeddings in groups with a small number of generators. We show that each finitely generated group $G$ lying in a variety ${\mathcal M}$ can be embedded in a $4$-generated group $H \in…

Let $A$ be a commutative noetherian ring, containing a field $k$, with $1/2\in k$, $\dim A=d$, and let $P$ be a projective $A$-module or $rank(P)=n$. In continuation of \cite{MM}, we study Homotopy obstructions for $P$ to split off a free…

We show that the abelian monoid of isomorphism classes of G-stable finite S-sets is free for a finite group G with Sylow p-subgroup S; here a finite S-set is called G-stable if it has isomorphic restrictions to G-conjugate subgroups of S.…

Let $G$ be a finite group of order $n$, and $Z_G=\mathbb{Z}\langle\zeta_{i,g}\mid g\in G,\ i=1,2,\dots,n\rangle$ be the free generic algebra, with canonical action of $G$ according to $(\zeta_{i,g})^x=\zeta_{i,x^{-1}g}$. It is proved that…

We prove a generalisation of the correspondence, due to Resende and Lawson--Lenz, between \'etale groupoids---which are topological groupoids whose source map is a local homeomorphisms---and complete pseudogroups---which are inverse monoids…

We show that Submonoid Membership is decidable in n-dimensional lamplighter groups $(\mathbb{Z}/p\mathbb{Z}) \wr \mathbb{Z}^n$ for any prime $p$ and integer $n$. More generally, we show decidability of Submonoid Membership in semidirect…

Unbounded entailment relations, introduced by Paul Lorenzen (1951), are a slight variant of a notion which plays a fundamental r\^ole in logic (see Scott 1974) and in algebra (see Lombardi and Quitt\'e 2015). We call systems of ideals their…

A poset is said to be (2+2)-free if it does not contain an induced subposet that is isomorphic to 2+2, the union of two disjoint 2-element chains. Two elements in a poset are indistinguishable if they have the same strict up-set and the…

In this article we prove several important results on graded rings, especially monoid-rings, that are motivated and inspired by Kaplansky's zero-divisor, unit and idempotents conjectures. Among the main results, we first generalize…

A marked free monoid morphism is a morphism for which the image of each generator starts with a different letter, and immersions are the analogous maps in free groups. We show that the (simultaneous) PCP is decidable for immersions of free…

A semigroup $S$ is said to be right pseudo-finite if the universal right congruence can be generated by a finite set $U\subseteq S\times S$, and there is a bound on the length of derivations for an arbitrary pair $(s,t)\in S\times S$ as a…

We introduce the notion of Universally Decodable Matrices of Genus g (UDMG), which for g=0 reduces to the notion of Universally Decodable Matrices (UDM) introduced in [8]. A UDMG is a set of L matrices over a finite field, each with K rows,…

In this paper we describe finitely generated groups $H$ universally equivalent (with constants from $G$ in the language) to a given torsion-free relatively hyperbolic group $G$ with free abelian parabolics. It turns out that, as in the free…

For a monoid $M$, we denote by $\mathbb G(M)$ the group of units, $\mathbb E(M)$ the submonoid generated by the idempotents, and $\mathbb G_L(M)$ and $\mathbb G_R(M)$ the submonoids consisting of all left or right units. Writing $\mathcal…

Recent research of the author has given an explicit geometric description of free (two-sided) adequate semigroups and monoids, as sets of labelled directed trees under a natural combinatorial multiplication. In this paper we show that there…

The full-domain partition monoid $P_n^{fd}$ has been discovered independently in two recent studies on connections between diagram monoids and category theory. It is a right restriction Ehresmann monoid, and contains both the full…