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arXiv · 1911.06076

The Boolean intervals of Chevalley type are strongly non group-complemented

Sebastien Palcoux·Pablo Spiga
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Abstract

Let G be a finite Chevalley group and B a Borel subgroup. Then the interval [B,G] in L(G) is Boolean. We prove, using Zsigmondy's theorem, that for any element P in the open interval (B,G), its lattice-complement P^c is not a group-complement.

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Sebastien Palcoux, Pablo Spiga. 2019-11-14. The Boolean intervals of Chevalley type are strongly non group-complemented. https://arxiv.org/abs/1911.06076

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