Related papers: Enumerating limit groups: A Corrigendum

This is a sequel to arXiv:1308.3604. We study applications to limit multiplicity generalizing the results of arXiv:1208.2257.

Let $c$ be the family of irreducible representations of a Weyl group $W$ corresponding to a two-sided cell of $W$. We define a subset $A_c$ of $c$ which contains the special representation of $W$ in $c$ and is in canonical bijection with…

We describe the fully residually F; or limit groups relative to F; (where F is a free group) that arise from systems of equations in two variables over F that have coefficients in F.

We present a dataset of word usage graphs (WUGs), where the existing WUGs for multiple languages are enriched with cluster labels functioning as sense definitions. They are generated from scratch by fine-tuned encoder-decoder language…

A group $G$ is called subgroup conjugacy separable if for every pair of non-conjugate finitely generated subgroups of $G$, there exists a finite quotient of $G$ where the images of these subgroups are not conjugate. We prove that limit…

Let $T$ be a (first order complete) dependent theory, ${\mathfrak{C}}$ a $\bar\kappa$-saturated model of $T$ and $G$ a definable subgroup which is abelian. Among subgroups of bounded index which are the union of $<\bar\kappa$ type definable…

A key challenge in citation text generation is that the length of generated text often differs from the length of the target, lowering the quality of the generation. While prior works have investigated length-controlled generation, their…

We define reflective numbers and their iterative summations. We provide classification of reflective numbers based on their iterative cyclical limits.

Given a finite group $G$, we denote by $L(G)$ the subgroup lattice of $G$ and by ${\rm Isolated}(G)$ the set of isolated subgroups of $G$. In this note, we describe finite groups $G$ such that $|{\rm Isolated}(G)|=|L(G)|-k$, where…

A finite group G is said to be a cut group if all central units in the integral group ring ZG are trivial. In this article, we extend the notion of cut groups, by introducing extended cut groups. We study the properties of extended cut…

This paper is a set of notes that we wrote concerning the first version of Emergent Gravity [gr-qc/0602022]. It is our version of an exercise that we proposed to some of our students. The idea was to find mathematical errors and…

We prove that if $G$ is a free-torsion group and $w(t)$ is a word in the alphabet $G \sqcup \{t^{\pm 1}\}$ with exponent sum one, then the group $<G,t|(w(t))^k = 1>$, where $k \geq 2$, is relatively hyperbolic with respect to $G$.

We give a brief introduction to the notion of an 'approximate group' and some of its numerous applications.

I study the measurement of scientists' influence using bibliographic data. The main result is an axiomatic characterization of the family of citation-counting indices, a broad class of influence measures which includes the renowned h-index.…

We perform the computations necessary to establish a multiplicity one statement for the irreducible representations of a finite spin group which in turn yields the classification of irreducible representations of finite spin groups. (The…

Formal languages based on the multiplication tables of finitely generated groups are investigated and used to give a linguistic characterization of word hyperbolic groups.

We analyse the two definitions of generalized quantifiers for logics of dependence and independence that have been proposed by F. Engstr\"om, comparing them with a more general, higher-order definition of team quantifier. We show that…

Lower bounds for some explicit decision problems over the complex numbers are given.

We define a semantics for first-order logic with generalized quantifiers based on double teams. We also define and investigate a notion of a generalized atom. Such atoms can be used in order to define extensions of first-order logic with a…

This paper is a survey on the works [MS77, MS79, MS81] on maximal subgroups in finitely generated linear groups, and the works that followed it [GG08, GG13b, GG13a, Kap03, Iva92, HO16, GM16, AGS14, Sf90, Sf98, Per05, AKT16, FG18, GS17]…