English

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

Group Theory 2019-11-15 v1 Combinatorics

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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Cite

@article{arxiv.1911.06076,
  title  = {The Boolean intervals of Chevalley type are strongly non group-complemented},
  author = {Sebastien Palcoux and Pablo Spiga},
  journal= {arXiv preprint arXiv:1911.06076},
  year   = {2019}
}

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4 pages