On a construction of A. Lucchini

2011/06/22 by Colin D. Reid, Reid, Colin D.
Engineering · Mathematics · #Advanced Control Systems Optimization #Mathematical Dynamics and Fractals #math.GR

paper · pdf · doi:10.48550/arxiv.1106.4423

2 pages

arxiv created 2011/06/22 · arxiv updated 2011/06/23

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.

Related

• On (hereditarily) just infinite profinite groups that are not virtually pro-p
• On the structure of just infinite profinite groups
• Some aspects of profinite group theory
• Profinite groups with few conjugacy classes of elements of infinite order
• The strong profinite genus of a finitely presented group can be infinite