Graded left modular lattices are supersolvable
arXiv:math/0404544
Abstract
We provide a direct proof that a finite graded lattice with a maximal chain of left modular elements is supersolvable. This result was first established via a detour through EL-labellings in [McNamara-Thomas] by combining results of McNamara and Liu. As part of our proof, we show that the maximum graded quotient of the free product of a chain and a single-element lattice is finite and distributive.
7 pages; 2 figures. Version 2: typos and a small error corrected; diagrams prettier; exposition improved following referee's suggestions; version to appear in Algebra Universalis