Large hereditarily just infinite groups. (Q986067)

The author gives a criterion for an inverse limit of a sequence of finite groups to be hereditarily just infinite, and a similar criterion for direct limits. He then uses this criterion to give constructions of hereditarily just infinite groups which satisfy required properties. In particular, the author constructs a hereditarily just infinite profinite group in which every countably based profinite group can be embedded (Theorem A). Thus demonstrating that a hereditarily just infinite profinite group need not be virtually pro-\(p\). Secondly the author constructs hereditarily just infinite prosoluble groups that are not (topologically) finitely generated (Theorem B). This is a useful paper which provides examples of hereditarily just infinite groups which enhance our understanding of these structures.