Commutators and pronilpotent subgroups in profinite groups

TL;DR

This paper investigates the structure of profinite groups where pronilpotent subgroups generated by commutators are periodic, proving that the derived subgroup is locally finite under these conditions.

Contribution

It establishes that in such profinite groups, the derived subgroup must be locally finite, advancing understanding of their subgroup structure.

Findings

G' is locally finite in the given conditions

Pronilpotent subgroups generated by commutators are periodic

Provides new insights into the structure of profinite groups

Abstract

Let G be a profinite group in which all pronilpotent subgroups generated by commutators are periodic. We prove that G' is locally finite.