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We describe the quasi-isometric classification of fundamental groups of irreducible non-geometric 3-manifolds which do not have "too many" arithmetic hyperbolic geometric components, thus completing the quasi-isometric classification of…
This paper is focused on numerical semigroups and presents a simple construction, that we call dilatation, which, from a starting semigroup $S$, permits to get an infinite family of semigroups which share several properties with $S$. The…
An integral domain is called atomic if every nonzero nonunit element factors into irreducibles. On the other hand, an integral domain is said to satisfy the ascending chain condition on principal ideals (ACCP) if every ascending chain of…
For some numerical semigroup rings of small embedding dimension, namely those of embedding dimension 3, and symmetric or pseudosymmetric of embedding dimension 4, presentations has been determined in the literature. We extend these results…
The recent proof of the Boij-Soederberg conjectures reveals new structure about Betti diagrams of modules, giving a complete description of the cone of Betti diagrams. We begin to expand on this new structure by investigating the semigroup…
The full lattices in a finite dimensional commutative ${\mathbb Q}$-algebra form a commutative semigroup. In the case of an algebraic number field the top part of a certain quotient semigroup is the class group. For a separable algebra some…
We give a structural theorem for pseudofinite groups of finite centraliser dimension. As a corollary, we observe that there is no finitely generated pseudofinite group of finite centraliser dimension.
We review the definition of hypergroups by Sunder, and we associate a hypergroup to a type III subfactor $N\subset M$ of finite index, whose canonical endomorphism $\gamma\in\mathrm{End}(M)$ is multiplicity-free. It is realized by positive…
We use a recent result of Bader and Sauer on coboundary expansion to prove residually finite three-dimensional Poincar\'e duality groups never have property (T). This implies such groups are never K\"ahler. The argument applies to…
The monogenic free inverse semigroup $FI_1$ is not finitely presented as a semigroup due to the classic result by Schein (1975). We extend this result and prove that a finitely generated subsemigroup of $FI_1$ is finitely presented if and…
Under suitable conditions on a family $(I(t))_{t\ge 0}$ of Lipschitz mappings on a complete metric space, we show that up to a subsequence the strong limit $S(t):=\lim_{n\to\infty}(I(t 2^{-n}))^{2^n}$ exists for all dyadic time points $t$,…
We investigate the notion of partial trace ideals, recently introduced by Maitra. We first establish several properties of partial trace ideals and give affirmative answers to questions posed by Maitra. We then study the invariant defined…
We consider the 3-manifold invariant I(M) which is defined by means of the Chern-Simons quantum field theory and which coincides with the Reshetikhin-Turaev invariant. We present some arguments and numerical results supporting the…
A topological group is minimal if it does not admit a strictly coarser Hausdorff group topology. We provide a sufficient and necessary condition for the minimality of the semidirect product $G\leftthreetimes P,$ where $G$ is a compact…
We first obtain explicit upper bounds for the proportion of elements in a finite classical group G with a given characteristic polynomial. We use this to complete the proof that the proportion of elements of a finite classical group G which…
We investigate the minimal number of generators $\mu$ and the depth of divisorial ideals over normal semigroup rings. Such ideals are defined by the inhomogeneous systems of linear inequalities associated with the support hyperplanes of the…
This is part of an ongoing project to find a general algebraic framework for semiring theory. The structure theory of semirings is quite challenging, largely because of the lack of negation, and such basic properties such as unique…
In 1976 S. Eilenberg and M.-P. Sch\"{u}tzenberger posed the following diabolical question: if $\mathbf{A}$ is a finite algebraic structure, $\Sigma$ is the set of all identities true in $\mathbf{A}$, and there exists a finite subset $F$ of…
We show that an infinite residually finite boundedly generated group has an infinite chain of finite index subgroups with ranks uniformly bounded, and give (sublinear) upper bounds on the ranks of arbitrary finite index subgroups of…
This paper is the continuation of \cite{CXY}. Let ${\bf G}$ be a simply connected semisimple algebraic group over $\Bbbk=\bar{\mathbb{F}}_q$, the algebraically closure of $\mathbb{F}_q$ (the finite field with $q=p^e$ elements), and $F$ be…