Geodesic
Chain Conditions for Modular Lattices with Finite Group Actions
Canadian journal of mathematics, Tome 31 (1979) no. 3, pp. 558-564

Voir la notice de l'article provenant de la source Cambridge University Press

This paper establishes the following combinatorial result concerning the automorphisms of a modular lattice.THEOREM. Let M be a modular lattice and let G be a finite subgroup of the automorphism group of M. If the sublattice, MG, of (common) fixed points (under G) satisfies any of a large class of chain conditions, then M satisfies the same chain condition. Some chain conditions in this class are the following: the ascending chain condition; the descending chain condition; Krull dimension; the property of having no uncountable chains, no chains order-isomorphic to the rational numbers; etc. 
Fisher, Joe W. Chain Conditions for Modular Lattices with Finite Group Actions. Canadian journal of mathematics, Tome 31 (1979) no. 3, pp. 558-564. doi: 10.4153/CJM-1979-058-9
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