On hereditarily just infinite profinite groups obtained via iterated wreath products

TL;DR

This paper investigates a broad class of hereditarily just infinite profinite groups, extending Wilson's work, and demonstrates that many of these groups have finite lower rank and are not topologically finitely presentable.

Contribution

It generalizes Wilson's family of groups, showing the existence of groups with finite lower rank and non-finite presentability within this class.

Findings

Contains groups of finite lower rank

Many are not topologically finitely presentable

Extends Wilson's family of groups

Abstract

We study a generalisation of the family of non-(virtually pro-$p$) hereditarily just infinite profinite groups introduced by J.\! S.\! Wilson in 2010. We prove that this family contains groups of finite lower rank. We also show that many groups in this family are not topologically finitely presentable.