On the Lower Garland of Certain Subgroup Lattices in Linear Groups

Details On the Lower Garland of Certain Subgroup Lattices in Linear Groups On the Lower Garland of Certain Subgroup Lattices in Linear Groups

1999-03-07

arxiv.org/abs/math/9903039v2

Mathematics

Rings and Algebras

AmsTeX, 12 pages; minor corrections

Scientific paper

We describe here the lower garland of some lattices of intermediate subgroups in linear groups. The results are applied to the case of subgroup lattices in general and special linear groups over a class of rings, containing the group of rational points T of a maximal non-split torus in the corresponding algebraic group. It turns out that these garlands coincide with the interval of the whole lattice, consisting of subgroups between T and its normalizer.

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