Related papers: Infinite Permutation Groups
Recent results on finite open group transformations are reviewed.
We show that one can naturally describe elements of R. Thompson's finitely presented infinite simple group $V$, known by Thompson to have a presentation with four generators and fourteen relations, as products of permutations analogous to…
We study the group of all interval exchange transformations (IETs). We show that for every IET $S$, there exists a dense open set of admissible IETs that share a relation with $S$. This is an extension of a result published by Dahmani,…
The exterior degree of a finite group has been introduced in [P. Niroomand and R. Rezaei, On the exterior degree of finite groups, Comm. Algebra 39 (2011), 335--343] and the present paper is devoted to study the exterior degree of infinite…
A triangle group is denoted by $\Delta(p,q,r)$ and has finite presentation $$ \Delta(p,q,r)=\langle x,y | x^p=y^q=(xy)^r=1 \rangle .$$ We examine a method for composition of permutation representations of a triangle group $\Delta(p,q,r)$…
These are extended notes based on lectures given by Vincent Franjou, Paul Sobaje, Peter Symonds and Antoine Touz\'e at the Master Class on New Developments in Finite Generation of Cohomology that took place at Bielefeld University in…
We consider the permutation group algebra defined by Cameron and show that if the permutation group has no finite orbits, then no homogeneous element of degree one is a zero-divisor of the algebra. We proceed to make a conjecture which…
An infinite permutation is a linear order on the set N. We study the properties of infinite permutations generated by fixed points of some uniform binary morphisms, and find the formula for their complexity.
These notes are based on a lecture course by L. Chekhov held at the University of Manchester in May 2006 and February-March 2007. They are divulgative in character, and instead of containing rigorous mathematical proofs, they illustrate…
We introduce the anonymity group, the neutrality group and the symmetry group of a social preference function. Inspired by a problem posed by Kelly in 1991 and remained unsolved, we investigate the problem of recognizing which permutation…
We show that many infinite classes of permutations over finite fields can be constructed via translators with a large choice of parameters. We first charac- terize some functions having linear translators, based on which several families of…
While general quantum field theories (QFTs) have yet to be rigorously defined in mathematics, they have generated new mathematics and have served as a unifying principle connecting different branches of the subject. In 1989, Witten made a…
This article is a summary of a talk about Richard Feynman, given at a conference Polymaths across the Eras organized in November 2023 by the St Cross Centre for the History and Philosophy of Physics (HAPP) in Oxford. It describes Feynman as…
Our aim is to describe the theory of Cartesian decompositions preserved by some member of a large family of finite transitive permutation groups called innatelytransitive groups.
This text follows the line of a talk on Ringberg symposium dedicated to Wolfhart Zimmermann 70th birthday. The historical overview (Part 1) partially overlaps with corresponding text of my previous commemorative paper. At the same time…
The notion of bounded FC-nilpotent group is introduced and it is shown that any such group is nilpotent-by-finite, generalizing a result of Neumann on bounded FC-groups.
This text is an extended version of the lecture notes for a course on representation theory of finite groups that was given by the authors during several years for graduate and postgraduate students of Novosibirsk State University and…
We study groups generated by sets of pattern avoiding permutations. In the first part of the paper we prove some general results concerning the structure of such groups. In the second part we carry out a case-by-case analysis of groups…
The Fourier Transform is one of the most important linear transformations used in science and engineering. Cooley and Tukey's Fast Fourier Transform (FFT) from 1964 is a method for computing this transformation in time $O(n\log n)$. From a…
The goal of this modern presentation, followed by an English translation from the German, is to make available some parts of Lie's very systematic mathematical thought which deserve to join the contemporary literature, and above all also,…