Related papers: Groups of Intermediate Growth: an Introduction for…
We introduce orbital graphs and discuss some of their basic properties. Then we focus on their usefulness for search algorithms for permutation groups, including finding the intersection of groups and the stabilizer of sets in a group.
An introduction to Hyperbolic Analysis is presented.
In this article we show how Gr\"un's results in group theory can be used for studying the structure of class groups in normal extensions.
In this book we introduce the notion of interval semigroups using intervals of the form [0, a], a is real. Several types of interval semigroups like fuzzy interval semigroups, interval symmetric semigroups, special symmetric interval…
Planning to explore the beginning of the Universe? A lightweight introductory guide to the theory of Inflation.
We give two new examples of groups of intermediate growth, by a method that was first used by Bux and P\'erez. Our examples are the groups generated by the automata with the kneading sequences 11(0) and 0(011). By results of Nekrashevych,…
This paper is the first of a series of introductory papers on the fascinating world of Soergel bimodules. It is combinatorial in nature and should be accessible to a broad audience. The objective of this paper is to help the reader feel…
We calculate extensions between certain irreducible admissible representations of p-adic groups.
This note constructs a finitely generated group $W$ whose word-growth is exponential, but for which the infimum of the growth rates over all finite generating sets is 1 -- in other words, of non-uniformly exponential growth. This answers a…
We survey new results on finite groups of birational transformations of algebraic varieties.
The purpose of this text is to set up a few basic notions concerning quantum graphs, to indicate some areas addressed in the quantum graph research, and to provide some pointers to the literature. The pointers in many cases are secondary,…
Lecture notes on an introductory course on arithmetic lattices (EPFL 2014).
The aim of this paper is to present the main constructions of the substructures of an almost groupoid and to discuss their basic properties. The definitions and properties concerning these new algebraic constructions extend to almost…
We indicate a natural generalization of the concept of subgroup commutativity degree of a finite group and a list of open problems on these new concepts.
We prove that the so called Grigorchuk-Maki group of intermadiate growth can be seen as a group of $C^1$ diffeomorphisms of the interval. On the other hand, we prove that every group of $C^{1+\alpha}$ diffeomorphisms of the interval having…
We consider abelain subgroups of small index in finite groups. More generally, we consider subgroups such that the product of their index by the index of their centralizer is small.
We describe groups elementarily equivalent to a free metabelian group with n generators. We also explore an exponentiation that naturally occurs in metabelian groups.
We introduce the notion of numerical semigroups generated by concatenation of arithmetic sequences and show that this class of numerical semigroups exhibit multiple interesting behaviours.
We give a criterion on pairs $(G,S)$ - where $G$ is a virtually $s$-step nilpotent group and $S$ is a finite generating set - saying whether the geodesic growth is exponential or strictly sub-exponential. Whenever $s=1,2$, this goes further…
Finding the number of maximal subgroups of infinite index of a finitely generated group is a natural problem that has been solved for several classes of `geometric' groups (linear groups, hyperbolic groups, mapping class groups, etc). Here…