Graded left modular lattices are supersolvable

2004/04/30 by Hugh Thomas, Thomas, Hugh
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #math.CO #msc:06B05 #msc:06B25

paper · pdf · doi:10.48550/arxiv.math/0404544

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

arxiv created 2004/10/12 · arxiv updated 2009/12/01

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.

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