Graded left modular lattices are supersolvable

Details Graded left modular lattices are supersolvable Graded left modular lattices are supersolvable

2004-04-30

arxiv.org/abs/math/0404544v2

Mathematics

Combinatorics

7 pages; 2 figures. Version 2: typos and a small error corrected; diagrams prettier; exposition improved following referee's s

Scientific paper

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.

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