Maximal intersections in finite groups

TL;DR

This paper studies four invariants related to the structure of the lattice of intersections of maximal subgroups in finite groups, revealing new insights into their behavior and relationships.

Contribution

It introduces and analyzes four invariants of finite groups that measure the complexity of the lattice of maximal subgroup intersections, providing new structural understanding.

Findings

Analysis of the invariants' properties and relationships.

Characterization of groups based on these invariants.

Insights into the lattice structure of maximal subgroup intersections.

Abstract

For a finite group $G$, we investigate the behaviour of four invariants, $\text{MaxDim}(G),$ $\text{MinDim}(G),$ $\text{MaxInt}(G)$ and $\text{MinInt}(G),$ measuring in some way the width and the height of the lattice $\mathcal M(G)$ consisting of the intersections of the maximal subgroups of $G.$