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Graded left modular lattices are supersolvable

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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 [MT] by combining results of McNamara [Mc] and Liu [Li]. 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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  1. Hugh Thomas

    Present address: Department of Mathematics and Statistics, University of New Brunswick, Fredericton, NB, E3B 5A3, Canada

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  1. Fields Institute, 222 College Street, Toronto, ON, M5T 3J1, Canada

    Hugh Thomas

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  1. Hugh Thomas
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Received May 24, 2004; accepted in final form October 12, 2004.

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Thomas, H. Graded left modular lattices are supersolvable. Algebra univers. 53, 481–489 (2005). https://doi.org/10.1007/s00012-005-1914-4

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  • DOI: https://doi.org/10.1007/s00012-005-1914-4

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