2009/06/26 by Colin D. Reid, Colin Reid · 13 citations
Mathematics · #Combinatorics #Discrete mathematics #Finite Group Theory Research #Finitely-generated abelian group #Geometric and Algebraic Topology #Group (periodic table) #Infinite group #Mathematics #Normal subgroup #Profinite group #Property (philosophy) #Pure mathematics #Rings, Modules, and Algebras #math.GR
paper · pdf · doi:10.1016/j.jalgebra.2010.07.034
published in Journal of Algebra 324(9), 2249-2261 (Elsevier BV) · 16 pages
arxiv created 2009/06/26 · openalex publication_date 2010/08/12 · arxiv updated 2010/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A profinite group G is just infinite if every closed normal subgroup of G is of finite index. We prove that an infinite profinite group is just infinite if and only if, for every open subgroup H of G, there are only finitely many open normal subgroups of G not contained in H. This extends a result recently established by Barnea, Gavioli, Jaikin-Zapirain, Monti and Scoppola, who proved the same characterisation in the case of pro-p groups. We also use this result to establish a number of features of the general structure of profinite groups with regard to the just infinite property.