Work

A Subgroup Lattice of a Finite Soluble Group

Year: 2026

Type: article

Abstract: A subgroup R of a finite group G is called weakly subnormal in G if R is not subnormal in G but it is subnormal in every proper overgroup of R in G . In this paper, weak subnormality is used to construct a subgroup lattice of a finite soluble group containing the lattice of all subnormal subgroups. A new characterisation of Schmidt groups is also obtained: they are exactly those groups with all subgroups subnormal or weakly subnormal.

Source: Bulletin of the Australian Mathematical Society

DOI: 10.1017/s0004972726101105

Authors: A. BALLESTER-BOLINCHES, S. F. KAMORNIKOV, O. L. SHEMETKOVA

Institutions: Universitat de València, Francisk Skorina Gomel State University, Plekhanov Russian University of Economics

Language: English

Topic: Finite Group Theory Research

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,550

Funders: Belarusian Republican Foundation for Fundamental Research, Generalitat Valenciana, European Regional Development Fund, Agencia Estatal de Investigación