Inverse system characterizations of the (hereditarily) just infinite property in profinite groups

TL;DR

This paper provides criteria for inverse systems of finite groups to produce just infinite or hereditarily just infinite profinite groups, establishing that all such groups can be obtained as limits of these systems.

Contribution

It introduces universal criteria for inverse systems that characterize all (hereditarily) just infinite profinite groups, correcting previous work.

Findings

Criteria ensure the limit is (hereditarily) just infinite

All such profinite groups arise as limits of these inverse systems

Provides a revised, corrected version of earlier results

Abstract

We give criteria on an inverse system of finite groups that ensure the limit is just infinite or hereditarily just infinite. More significantly, these criteria are 'universal' in that all (hereditarily) just infinite profinite groups arise as limits of the specified form. This is a corrected and revised version of the article: 'Inverse system characterizations of the (hereditarily) just infinite property in profinite groups', Bull. LMS vol 44, 3 (2012) 413--425.