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Alexandre Borovik

Publications and source records attributed to Alexandre Borovik.

38 records · Page 3Linked to original sources
arXiv2007

A New Trichotomy Theorem

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.

math.GR↗
arXiv2007

Uniqueness cases in odd type groups of finite Morley rank

Here we analyze a proper 2-generated core in a minimal counter example to the Cherlin-Zilber Algebraicity Conjecture for simple groups of finite Morley rank. We ultimately show that such a group is strongly embedded and the ambiant group is minimal connected simple.

math.GR↗