TL;DR
This paper proves that a specific profinite group constructed by A. Lucchini is hereditarily just infinite and contains all countably based profinite groups as closed subgroups, expanding understanding of its structure.
Contribution
It establishes the hereditary just infiniteness of Lucchini's group and its universality for countably based profinite groups, clarifying its structural properties.
Findings
Lucchini's group is hereditarily just infinite.
The group contains every countably based profinite group as a closed subgroup.
The result clarifies the structure of the group constructed by Lucchini.
Abstract
We show that the group constructed in the 2004 paper 'A 2-generated just-infinite profinite group which is not positively finitely generated' by A. Lucchini is in fact hereditarily just infinite and contains every countably based profinite group as a closed subgroup. Lucchini's paper predates some related work of J. Wilson.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Control Systems Optimization