Tame minimal simple groups of finite Morley rank
نویسندگان
چکیده
منابع مشابه
On Weyl groups in minimal simple groups of finite Morley rank
We prove that generous non-nilpotent Borel subgroups of connected minimal simple groups of finite Morley rank are self-normalizing. We use this to introduce a uniform approach to the analysis of connected minimal simple groups of finite Morley rank through a case division incorporating four mutually exclusive classes of groups. We use these to analyze Carter subgroups and Weyl groups in connect...
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The Algebraicity Conjecture treats model-theoretic foundations of algebraic group theory. It states that any simple group of finite Morley rank is an algebraic group over an algebraically closed field. In the mid-1990s a view was consolidated that this project falls into four cases of different flavour: even type, mixed type, odd type, and degenerate type. This book contains a proof of the conj...
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The Algebraicity Conjecture states that a simple group of finite Morley rank should be isomorphic with an algebraic group. A program initiated by Borovik aims at controlling the 2-local structure in a hypothetical minimal counterexample to the Algebraicity Conjecture. There is now a large body of work on this program. A fundamental division arises at the outset, according to the structure of a ...
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Introduction. Zilber’s original trichotomy conjecture proposed an explicit classification of all one-dimensional objects arising in model theory. At one point, classifying the simple groups of finite Morley rank was viewed as a subproblem whose affirmative answer would justify this conjecture. Zilber’s conjecture was eventually refuted by Hrushovski [9], and the classification of simple groups ...
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Now assume |G : H| is infinite and that H is definable in G (but H need no longer be infinite or G-normal). Let Z = Z◦(G), and note that (a) implies that Z is infinite. If |Z : H ∩Z| is infinite, then |HZ : H| is infinite as well. In this case we are done since H ≤ HZ ≤ NG(H). Otherwise, |Z : H ∩Z| is finite, so the connectedness of Z implies that Z ≤ H. We can now proceed by induction on the r...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2004
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2003.12.027