On Two Classes of Sublattices of the Subgroup Lattice of a Finite Group
Abstract
Let G denote a finite group; σ={σi∣i∈I⊆{0}∪N} be some partition of the set of all primes P, where 0∈I; I be a class of finite σ0-groups that is closed under extensions, epimorphic images, and subgroups and contains all finite soluble σ0-groups. We say that a subgroup A of G is σI-subnormal in G if there is a subgroup chain A=A0≤A1≤⋯≤At=G such that either Ai−1⊴Ai, Ai/(Ai−1)Ai∈I, or Ai/(Ai−1)Ai is a σj-group for some j≠0. In this paper, we prove that the set LσI(G) of all σI-subnormal subgroups of G and some proper subsets of LσI(G) form sublattices of the lattice of all subgroups of G.
Fields of Study & Subjects
Finite Group Theory Research
Advanced Topics in Algebra
Rings
Modules
and Algebras
Publication details
- Journal / source
- Mathematics
- Volume
- 14
- Issue
- 2
- Pages
- 328–328
- Publication date
- 18 January 2026
- Language
- EN