A note on FC-nilpotency

TL;DR

This paper introduces the concept of bounded FC-nilpotent groups and proves that such groups are essentially nilpotent-by-finite, extending previous results on FC-groups.

Contribution

It generalizes Neumann's result by defining bounded FC-nilpotent groups and establishing their structure as nilpotent-by-finite.

Findings

Bounded FC-nilpotent groups are nilpotent-by-finite

Extension of Neumann's result to a broader class of groups

Introduction of the notion of bounded FC-nilpotency

Abstract

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.