Finite groups in which every cyclic subgroup is the intersection of maximal subgroups

TL;DR

This paper characterizes finite groups where each cyclic subgroup is an intersection of maximal subgroups, providing insights into their structural properties and comparing with groups where all proper subgroups have this property.

Contribution

It offers a complete structural classification of finite groups with the cyclic subgroup intersection property, expanding understanding of subgroup lattice configurations.

Findings

Characterization of finite groups with cyclic subgroup intersection property

Comparison with groups where all proper subgroups are intersections of maximal subgroups

Structural insights into subgroup lattice arrangements

Abstract

We determine the structure of the finite groups with the property that every cyclic subgroup is the intersection of maximal subgroups, comparing this property with the one where all proper subgroups are intersections of maximal subgroups.