Related papers: Inverse semigroups with rational word problem are …
A subsemigroup $S$ of an inverse semigroup $Q$ is a left I-order in $Q$ if every element in $Q$ can be written as $a^{-1}b$ where $a,b \in S$ and $a^{-1}$ is the inverse of $a$ in the sense of inverse semigroup theory. If we insist on $a$…
This paper focuses on a refinement of the inverse Galois problem. We explore what finite groups appear as the Galois group of an extension of the rational numbers in which only a predetermined set of primes may ramify. After presenting new…
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…
In this article we will study semigroupoids, and more specifically inverse semigroupoids. These are a common generalization to both inverse semigroups and groupoids, and provide a natural language on which several types of dynamical…
This note contains a report of a proof by computer that the Fibonacci group F(2,9) is automatic. The automatic structure can be used to solve the word problem in the group. Furthermore, it can be seen directly from the word-acceptor that…
It is proved that, given a (von Neumann) regular semigroup with finitely many left and right ideals, if every maximal subgroup is presentable by a finite complete rewriting system, then so is the semigroup. To achieve this, the following…
In this article we overview those aspects of the theory of affine semigroups and their algebras that have been relevant for our own research, and pose several open problems. Answers to these problems would contribute substantially to the…
We study systematically groups whose marked finite quotients form a recursive set. We give several definitions, and prove basic properties of this class of groups, and in particular emphasize the link between the growth of the depth…
Motivated by intuitive properties of physical quantities, the notion of a non-anomalous semigroup is formulated. These are totally ordered semigroups where there are no `infinitesimally close' elements. The real numbers are then defined as…
Two finitely generated groups have the same set of finite quotients if and only if their profinite completions are isomorphic. Consider the map which sends (the isomorphism class of) an S-arithmetic group to (the isomorphism class of) its…
This paper studies decision problems for semigroups that are word-hyperbolic in the sense of Duncan & Gilman. A fundamental investigation reveals that the natural definition of a `word-hyperbolic structure' has to be strengthened slightly…
In this paper, we classify finite categories with two objects such that one of the endomorphism monoids is a group. We prove that having a group on one side affects the structure of the other endomorphism monoid, and we prove that it is…
$\omega$-clones are multi-sorted structures that naturally emerge as algebras for infinite trees, just as $\omega$-semigroups are convenient algebras for infinite words. In the algebraic theory of languages, one hopes that a language is…
We present an impossibility result, called a theorem about facts and words, which pertains to a general communication system. The theorem states that the number of distinct words used in a finite text is roughly greater than the number of…
Let $A$ be a nonempty finite set of $k$ integers. Given a subset $B$ of $A$, the sum of all elements of $B$, denoted by $s(B)$, is called the subset sum of $B$. For a nonnegative integer $\alpha$ ($\leq k$), let \[\Sigma_{\alpha}…
Suppose that an infinite set $A$ occupies at most $\frac{1}{2}(p+1)$ residue classes modulo $p$, for every sufficiently large prime $p$. The squares, or more generally the integer values of any quadratic, are an example of such a set. By…
The object of this paper is to examine finite solvable groups whose integral group rings have only trivial central units.
We describe a new approach to the Word Problem for Artin-Tits groups and, more generally, for the enveloping group U(M) of a monoid M in which any two elements admit a greatest common divisor. The method relies on a rewrite system R(M) that…
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 extend the theory of fast Fourier transforms on finite groups to finite inverse semigroups. We use a general method for constructing the irreducible representations of a finite inverse semigroup to reduce the problem of computing its…