On the structure of groups with polynomial growth IV

TL;DR

This paper explores the structure of groups with polynomial growth, providing applications to growth functions, FC-G series, and related group classes, building on previous structure theorems for such groups.

Contribution

It extends the understanding of polynomial growth groups by applying the structure theorem to various growth functions and their relations to FC-G series, and explores related group classes.

Findings

Applications to various growth functions

Relations to FC-G series established

Results on related classes of groups

Abstract

Recently we have shown a structure theorem for locally compact groups of polynomial growth. We give now some applications on various growth functions and relations to FC-G - series. In addition, we show some results on related classes of groups.