On the prehistory of growth of groups

TL;DR

This paper reviews the historical development of group growth theory, highlighting its early influences and contributions prior to 1968 in both Soviet and Western mathematical research.

Contribution

It uncovers and discusses the early, overlooked instances where growth of groups was implicitly or explicitly studied before 1968.

Findings

Growth of groups was studied in various contexts before 1968.

Early works influenced later developments in geometric group theory.

Historical perspective on the evolution of group growth research.

Abstract

The subject of growth of groups has been active in the former Soviet Union since the early 50's and in the West since 1968, when articles of \v{S}varc and Milnor have been published, independently. The purpose of this note is to quote a few articles showing that, before 1968 and at least retrospectively, growth has already played some role in various subjects.