Pseudocomplementation in (Normal) Subgroup Lattices

Abstract

The goal of this article is to study finite groups admitting a pseudocomplemented subgroup lattice (PK-groups) or a pseudocomplemented normal subgroup lattice (PKN-groups). In particular, we obtain a complete classification of finite PK-groups and of finite nilpotent PKN-groups. We also study groups with a Stone normal subgroup lattice, and we classify finite groups for which every subgroup has a Stone normal subgroup lattice. Finally, we obtain a complete classification of finite groups for which every subgroup is monolithic.

Key Words:

• Monolithic group
• Normal subgroup lattice
• Pseudocomplement
• Stone lattice
• Subgroup lattice

2000 Mathematics Subject Classification:

• Primary 06D15, 20D30
• Secondary 20D15, 20D20

Notes

Communicated by M. Kambites.