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Uniqueness cases in odd type groups of finite Morley rank

By Re V. Borovik, Jeffrey Burdges and Ali Nesin


There is a longstanding conjecture, due to Gregory Cherlin and Boris Zilber, that all simple groups of finite Morley rank are simple algebraic groups. One of the major theorems in the area is Borovik’s trichotomy theorem. The “trichotomy ” here is a case division of the generic minimal counterexamples within odd type, i.e. groups whose Sylow ◦ 2-subgroup is large and divisible. The so-called uniqueness case the trichotomy theorem is the existence of a proper 2-generated core. It is our goal to drive presence of a proper 2-generated core to a contradiction; and hence bound the complexity of the Sylow ◦ 2-subgroup of a minimal counter example to the Cherlin-Zilber conjecture. This paper shows that the group in the question is a minimal connected simple group and has a strongly embedded subgroup, a far stronger uniqueness case. As a corollary, a tame counter example to the Cherlin-Zilber conjecture has Prüfer rank at most two

Year: 2004
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