Related papers: Enumerating limit groups: A Corrigendum

A new framework for a high energy limit of quantum gauge field theories is introduced. Its potency is illustrated on a new derivation of the reggeization of the gluon.

These notes deal with a few aspects of Lie algebras and Lie groups, including some matters related to exponentiation.

In the paper, a method of describing the outer derivations of the group algebra of a finitely presentable group is given. The description of derivations is given in terms of characters of the groupoid of the adjoint action of the group.

In this third paper in a series on type I Howe duality for finite fields, we give a complete description of the restriction of the oscillator representation over a finite field to products of dual pairs of symplectic and orthogonal groups…

We consider dense 2-generator multiplicative subgroups in $\mathbb C$ and show that for each point $z\in \mathbb C$ the set of limit values for the arguments of the powers of each generator at the point $z$ is either finite or is…

In this paper, we summarize the work on the characterization of finite simple groups and the study on finite groups with the set of element orders and two orders (the order of group and the set of element orders). Some related topics, and…

We give a geometric description of a certain class of epimorphisms between complex reflection groups. We classify these epimorphisms, which can be interpreted as ``morphisms'' between the diagrams symbolizing standard presentations by…

In one article, the author has defined an L-group associated to a cover of a quasisplit reductive group over a local or global field. In another article, Wee Teck Gan and Fan Gao define (following an unpublished letter of the author) an…

We present a modification of quantum mechanics with a *possible worlds* semantics. It is shown that `gauge' degrees of freedom along possible worlds can be used to encode gravitational information.

In this paper, we initiate a systematic study of entanglements of division fields from a group theoretic perspective. For a positive integer $n$ and a subgroup $G\subseteq \text{GL}_2(\mathbb{Z}/{n}\mathbb{Z})$ with surjective determinant,…

We calculate extensions between certain irreducible admissible representations of p-adic groups.

Let $G$ be a finite group and $\alpha(G)=\frac{|C(G)|}{|G|}$\,, where $C(G)$ denotes the set of cyclic subgroups of $G$. In this short note, we prove that $\alpha(G)\leq\alpha(Z(G))$ and we describe the groups $G$ for which the equality…

This is the first in a series of papers on type I Howe duality for finite fields, concerning the restriction of an oscillator representation of the symplectic group to a product of a symplectic and an orthogonal group. The goal of the…

If G is a finite group and H is a subgroup of G, we characterize when restriction of Brauer characters from G to H is injective.

The aim of the present article is to establish the connection between the existence of the limit along the normal and an admissible limit at a fixed boundary point for holomorphic functions of several complex variables.

This article discusses numerical semigroups having a generator which is as large as possible. This turns out to be $2g+1$, where $g$ is the genus of the semigroup. We will show that these semigroups are closely related to symmetric…

We study the impact of certain identities and probabilistic identities on the structure of finite groups. More specifically, let $w$ be a nontrivial word in $d$ distinct variables and let $G$ be a finite group for which the word map…

We give a complete list of the one-dimensional groups definable in algebraically closed valued fields and i the pseudo-local fields, up to a finite index subgroup and a quotient by a finite subgroup.

We propose a new line of attack to create a finite quantum theory which includes general relativity and (perhaps) the standard model in its low energy limit. The theory would emerge from the categorical approach. A structure is observed on…

We consider metric versions of the notions of local embeddability and LEF. We pay special attention to normally finitely generated groups with word metrics.