An EL-labeling of the subgroup lattice

TL;DR

This paper constructs an EL-labeling for the subgroup lattice of finite solvable groups, confirming a conjecture and providing a combinatorial tool for understanding subgroup structures.

Contribution

The paper provides the first explicit EL-labeling for subgroup lattices of finite solvable groups, confirming Shareshian's conjecture.

Findings

Successfully constructs an EL-labeling for subgroup lattices

Verifies the labeling has the expected properties

Supports Shareshian's conjecture with explicit construction

Abstract

In a 2001 paper, Shareshian conjectured that the subgroup lattice of a finite, solvable group has an EL-labeling. We construct such a labeling, and verify that our labeling has the expected properties.