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
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