Skip Garibaldi and Philippe Gille: Algebraic groups with few subgroups,

Submission: 2008, May 13

Every semisimple linear algebraic group over a field F contains nontrivial connected subgroups, namely maximal tori. In the early 1990s, J. Tits proved that some groups of type E_8 have no others. We give a simpler proof of his result, prove that some trialitarian groups of type have no nontrivial connected subgroups, and give partial results for types E_6 and E_7.

2000 Mathematics Subject Classification: 20G15

Keywords and Phrases: Linear algebraic groups, exceptional groups, Galois cohomology

Full text: dvi.gz 51 k, dvi 114 k, ps.gz 835 k, pdf.gz 245 k, pdf 275 k.

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