Related papers: Answering Five Open Problems Involving Semigroup C…

We consider pairs of finitely presented, residually finite groups $P\hookrightarrow\G$ for which the induced map of profinite completions $\hat P\to \hat\G$ is an isomorphism. We prove that there is no algorithm that, given an arbitrary…

In this article, we show that a group $G$ is the union of two proper subsemigroups if and only if $G$ has a nontrivial left-orderable quotient. Furthermore, if $G$ is the union of two proper semigroups, then there exists a minimum normal…

We study the connection between small-overlap conditions and automaticity of semigroups. We restrict the discussion to conditions that imply embeddability and under which each relation decomposes into at least seven pieces. For these…

Cross-connection is a construction of regular semigroups using certain categories called normal categories which are abstractions of the partially ordered sets of principal left (right) ideals of a semigroup. We describe the…

The existence of a semiconjugate relation permits the transformation of a higher order difference equation on a group into an equivalent triangular system of two difference equations of lower orders. Introducing time-dependent form…

It is often the case that a covering map of the open annulus is semiconjugate to a map of the circle of the same degree. We investigate this possibility and its consequences on the dynamics. In particular, we address the problem of the…

Let $G$ be a nonabelian group. We say that $G$ has an abelian partition, if there exists a partition of $G$ into commuting subsets $A_1, A_2, \ldots, A_n$ of $G$, such that $|A_i|\geqslant 2$ for each $i=1, 2, \ldots, n$. This paper…

A semigroup $S$ is called an equational domain if any finite union of algebraic sets over $S$ is algebraic. We prove if a completely regular semigroup $S$ is an equational domain then $S$ is completely simple.

We consider the following problem stated by Vdovin (2010) in the "Kourovka notebook" (Problem 17.41): Let $H$ be a solvable subgroup of a finite group $G$ that has no nontrivial solvable normal subgroups. Do there always exist five…

We define a notion of semi-conjugacy between orientation-preserving actions of a group on the circle, which for fixed point free actions coincides with a classical definition of Ghys. We then show that two circle actions are semi-conjugate…

In this article, we study connections between representation theory and efficient solutions to the conjugacy problem on finitely generated groups. The main focus is on the conjugacy problem in conjugacy separable groups, where we measure…

For every group $G$, the set $\mathcal{P}(G)$ of its subsets forms a semiring under set-theoretical union $\cup$ and element-wise multiplication $\cdot$ and forms an involution semigroup under $\cdot$ and element-wise inversion ${}^{-1}$.…

We give a definition of partition C*-algebras: To any partition of a finite set, we assign algebraic relations for a matrix of generators of a universal C*-algebra. We then prove how certain relations may be deduced from others and we…

We consider semigroup algorithmic problems in finitely generated metabelian groups. Our paper focuses on three decision problems introduced by Choffrut and Karhum\"{a}ki (2005): the Identity Problem (does a semigroup contain a neutral…

Composition and lattice join (transitive closure of a union) of equivalence relations are operations taking pairs of decidable equivalence relations to relations that are semi-decidable, but not necessarily decidable. This article addresses…

Let $G$ be a classical group defined over a finite field. We consider the following fundamental problems concerning conjugacy in $G$: 1. List a representative for each conjugacy class of $G$. 2. Given $x \in G$, describe the centralizer of…

We study conjugacy relations on semigroups and monoids, focusing on the relation $a \cfn b$, defined by the existence of $g,h \in S^1$ such that $ag = gb$, $bh = ha$, $hag = b$, and $gbh = a$. This notion emerged as one that yields…

We develop a structure theory of connected solvable spherical subgroups in semisimple algebraic groups. Based on this theory, we obtain an explicit classification of all such subgroups up to conjugation.

'A semigroup is completely regular if and only if it is a union of groups'- an analogue of this structure theorem of completely regular semigroup has been obtained in the setting of seminearrings in [[16], Mukherjee (Pal) et al., Semigroup…

A CP-semigroup is aligned if its set of trivially maximal subordinates is totally ordered by subordination. We prove that aligned spatial E_0-semigroups are prime: they have no non-trivial tensor product decompositions up to cocycle…