Results 141 to 150 of about 6,390 (190)

Primitive Permutation Groups of Finite Morley Rank

Proceedings of the London Mathematical Society, 1995
A version is given of the O'Nan-Scott Theorem for definably primitive permutation groups of finite Morley rank. This raises questions about structures of the form \((F,+, \cdot, H)\) where \((F, +, \cdot)\) is an algebraically closed field and \(H\) is a predicate for a central extension of a simple group, with \(H \leq \text{GL} (n,F)\). Among partial
D. Macpherson, A. Pillay
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Good tori in groups of finite Morley rank

Journal of Group Theory, 2005
Recall that a `torus' in a group of finite Morley rank is a definable divisible Abelian subgroup; it is `decent' if it is the definable hull of its torsion elements, and `good' if every definable subgroup is decent. The author shows that good tori have strong rigidity properties: (1) A connected definable group of automorphisms is trivial.
G. Cherlin
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Bad groups of finite Morley rank

Journal of Symbolic Logic, 1989
AbstractWe prove the following theorem. Let G be a connected simple bad group (i.e. of finite Morley rank, nonsolvable and with all the Borel subgroups nilpotent) of minimal Morley rank. Then the Borel subgroups of G are conjugate to each other, and if B is a Borel subgroup of G, then , NG(B) = B, and G has no involutions.
L. Corredor
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Around unipotence in groups of finite Morley rank

jgth, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Olivier Frécon
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Simple groups of finite morley rank and Tits buildings

Israel Journal of Mathematics, 1999
The Morley rank of a structure is a model-theoretic dimension function which measures the complexity of the definable subsets of that structure. Finiteness of the Morley rank is a strong condition. Indeed, the Cherlin-Zil'ber conjecture states that any infinite simple group \(G\) of finite Morley rank should be an algebraic group over an algebraically ...
L. Kramer, K. Tent, H. Maldeghem
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A Generic Identification Theorem for Groups of Finite Morley Rank

Journal of the London Mathematical Society, 2004
The paper contains a final identification theorem for the ‘generic’ K*‐groups of finite Morley rank.
A. Berkman, A. Borovik
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