2010/10/19 by Colin D. Reid, Reid, Colin D.
Computer Science · Mathematics · #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Rings, Modules, and Algebras #math.GR #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1010.3979
5 pages
openalex publication_date 2010/10/19 · arxiv created 2010/10/21 · arxiv updated 2010/10/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
A profinite group G is just infinite if every non-trivial closed normal subgroup of G is of finite index, and hereditarily just infinite if every open subgroup is just infinite. Hereditarily just infinite profinite groups need not be virtually pro-p, as shown in a recent paper of Wilson. The same paper gives a criterion on an inverse system of finite groups that is sufficient to ensure the limit is either virtually abelian or hereditarily just infinite. We give criteria of a similar nature that characterise the just infinite and hereditarily just infinite properties under the assumption that G is not virtually pro-p.