2026/07/31 by Fawaz Aseeri, Julian Kaspczyk
Computer Science · Mathematics · #Advanced Algebra and Logic #Characteristic subgroup #Finite Group Theory Research #Finite group #Fitting subgroup #Group (periodic table) #Lattice (music) #Locally finite group #Normal subgroup #Rings, Modules, and Algebras
paper · doi:10.1142/s0219498828500223
crossref issued 2026/07/31 · crossref published 2026/07/31 · crossref published-online 2026/07/31 · openalex publication_date 2026/07/31 · crossref created 2026/07/31 · crossref deposited 2026/07/31 · crossref indexed 2026/07/31 · openalex created_date 2026/08/01 · openalex updated_date 2026/08/01
A subgroup H of a finite group G is said to be an ICΦ-subgroup of G if H ∩ [H,G] ≤ Φ(H). We say that a finite group has dense ICΦ-subgroups if each non-empty open interval in its subgroup lattice contains an ICΦ-subgroup. In this note, we show that, under a few additional conditions, a finite group with dense ICΦ-subgroups is abelian.