Uniqueness cases in odd-type groups of finite Morley rank |
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Authors: | Borovik Alexandre V; Burdges Jeffrey; Nesin Ali |
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Institution: | School of Mathematics The University of Manchester PO Box 88, Sackville Street Manchester M60 1QD United Kingdom alexandre.borovik{at}umist.ac.uk |
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Abstract: | There is a longstanding conjecture, due to Gregory Cherlin andBoris Zilber, that all simple groups of finite Morley rank aresimple algebraic groups. One of the major theorems in the areais Borovik's trichotomy theorem. The trichotomyhere is a case division of the generic minimal counterexampleswithin odd type, that is, groups with a large and divisibleSylow° 2-subgroup. The so-called uniqueness casein the trichotomy theorem is the existence of a proper 2-generatedcore. It is our aim to drive the presence of a proper 2-generatedcore to a contradiction, and hence bind the complexity of theSylow° 2-subgroup of a minimal counterexample to the Cherlin–Zilberconjecture. This paper shows that the group in question is aminimal connected simple group and has a strongly embedded subgroup,a far stronger uniqueness case. As a corollary, a tame counterexampleto the Cherlin–Zilber conjecture has Prüfer rankat most two. |
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