Asymptotic Growth of Finite Groups

Abstract

We investigate word growth and structure of certain infinite families of finite groups. This work is motivated by results of Bass, Wolf, Milnor, Gromov, and Grigorchuk on the word growth and structure of infinite groups. We define word growth for families of finite groups, and prove structure theorems relating their growth types to their group structures. Some results are analogous to the infinite cases. However, differences are also noted, as well as other results. © 1998 Academic Press.