Related papers: On the prehistory of growth of groups

We present a survey of results related to the Milnor's problem on group growth. We discuss the cases of polynomial growth, exponential but not uniformly exponential growth, but the main part of the article is devoted to the intermediate…

In this Digest we review a recent study released by the Google Scholar team on the apparently increasing fraction of citations to old articles from studies published in the last 24 years (1990-2013). First, we describe the main findings of…

In this paper, we examine the evolution of the impact of older scholarly articles. We attempt to answer four questions. First, how often are older articles cited and how has this changed over time. Second, how does the impact of older…

These are introductory notes on word growth of groups, and include a gentle presentation of wreath products as well as recent results on construction of groups of with given growth function. They are are an expanded version of a mini-course…

The theory of one-relator groups is now almost a century old. The authors therefore feel that a comprehensive survey of this fascinating subject is in order, and this document is an attempt at precisely such a survey. This article is…

This is a brief introduction to the study of growth in groups of Lie type, with $SL_2(\mathbb{F}_q)$ and some of its subgroups as the key examples. They are an edited version of the notes I distributed at the Arizona Winter School in 2016.…

This paper provides the first historical analysis of the relationship between collaboration and scientific impact, using three indicators of collaboration (number of authors, number of addresses, and number of countries) and including…

This is a short survey of the progress on the congruence subgroup problem since the sixties when the first major results on the integral unimodular groups appeared. It is aimed at the non-specialists and avoids technical details.

This is a short introduction (in Spanish) to the study of growth in finite groups, with SL_2 as an example. Emphasis is put on developments of the decade 2005--2015, originating partly in combinatorics. Little algebraic-geometrical…

This is a survey of methods developed in the last few years to prove results on growth in non-commutative groups. These techniques have their roots in both additive combinatorics and group theory, as well as other fields. We discuss linear…

We generalize a class of groups defined by Rostislav Grigorchuk to a much larger class of groups, and provide upper and lower bounds for their word growth (they are all of intermediate growth) and period growth (under a small additional…

Social groups are fundamental elements of any social system. Their emergence and evolution are closely related to the structure and dynamics of a social system. Research on social groups was primarily focused on the growth and the structure…

In this paper we retrace the recent history of statistics by analyzing all the papers published in five prestigious statistical journals since 1970, namely: Annals of Statistics, Biometrika, Journal of the American Statistical Association,…

This survey aims to cover the motivation for and history of the study of local rigidity of group actions. There is a particularly detailed discussion of recent results, including outlines of some proofs. The article ends with a large number…

International collaboration as measured by co-authorship relations on refereed papers grew linearly from 1990 to 2005 in terms of the number of papers, but exponentially in terms of the number of international addresses. This confirms…

This paper studies the evolution of the distribution of opinions in a population of individuals in which there exist two distinct subgroups of highly-committed, well-connected opinion leaders endowed with a strong convincing power. Each…

Evolutionary role of the separation into two sexes from a cyberneticist's point of view. [I translated this 1965 article from Russian "Nauka i Zhizn" (Science and Life) in 1988. In a popular form, the article puts forward several useful…

Human communities have self-organizing properties in which specific Dunbar Numbers may be invoked to explain group attachments. By analyzing Wikipedia editing histories across a wide range of subject pages, we show that there is an emergent…

P.W. Anderson proposed the concept of complexity in order to describe the emergence and growth of macroscopic collective patterns out of the simple interactions of many microscopic agents. In the physical sciences this paradigm was…

The growth of a finitely generated group is an important geometric invariant which has been studied for decades. It can be either polynomial, for a well-understood class of groups, or exponential, for most groups studied by geometers, or…