2007/11/27 by Alexandre Borovik, Borovik, Alexandre, Jeffrey Burdges +1
Mathematics · #03C60 #20G99 #FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO) #math.GR #math.LO #msc:03C60 #msc:20G99
paper · pdf · doi:10.48550/arxiv.0711.4169
arxiv created 2007/11/27 · arxiv updated 2009/12/01
We show that a minimal counter example to the Cherlin-Zilber Algebraicity Conjecture for simple groups of finite Morley rank has normal 2-rank at most two, which is a tameness free version of Borovik's original trichotomy theorem. This result serves as a bridge by showing that there are no groups found strictly between the generic and quasithin cases, i.e. between groups of Lie rank at least three, and groups of Lie rank one and two. Again this result depends upon previous work for the uniqueness case analysis.