What question did this study set out to answer?

This paper aims to explore weak subnormality and its applications in constructing subgroup lattices of finite soluble groups.

March 31, 2026Open Access

A Subgroup Lattice of a Finite Soluble Group

ABA. BALLESTER-BOLINCHESUniversitat de València SKS. F. KAMORNIKOVFrancisk Skorina Gomel State University OSO. L. SHEMETKOVAPlekhanov Russian University of Economics

Key Points

This paper aims to explore weak subnormality and its applications in constructing subgroup lattices of finite soluble groups.
Defined weakly subnormal subgroups in finite groups.
Constructed a subgroup lattice including all subnormal subgroups.
Developed a characterization of Schmidt groups in terms of subgroup properties.
Established a subgroup lattice encompassing all subnormal subgroups in finite soluble groups.
Identified Schmidt groups as those groups where all subgroups are weakly subnormal or subnormal.

Abstract

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.

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