Results 11 to 20 of about 6,390 (190)
Involutions in groups of finite Morley rank of degenerate type [PDF]
, 2007 .In a connected group of finite Morley rank, if the Sylow 2-subgroups are finite then they are trivial. The proof involves a combination of model-theoretic ideas with a device originating in black box group theory.
A. Borovik, Jeffrey Burdges, G. Cherlin
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The Bender method in groups of finite Morley rank [PDF]
Journal of Algebra, 2007 Jaligot's Lemma states that the Fitting subgroups of distinct Borel subgroups do not intersect in a tame minimal simple groups of finite Morley. Such a strong result appears hopeless without tameness. Here we use the 0-unipotence theory to build a toolkit for the analysis of nonabelian intersections of Borel subgroups.
Jeffrey Burdges
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A signalizer functor theorem for groups of finite Morley rank [PDF]
Journal of Algebra, 2003 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 minimal counterexamples within odd type, i.e.
Jeffrey Burdges
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Mock hyperbolic reflection spaces and Frobenius groups of finite Morley rank [PDF]
Model Theory, 2021 We define the notion of mock hyperbolic reflection spaces and use it to study Frobenius groups, in particular in the context of groups of finite Morley rank including the so-called bad groups. We show that connected Frobenius groups of finite Morley rank
Tim Clausen, K. Tent
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Groups of Finite Morley Rank with a Pseudoreflection Action [PDF]
Journal of Algebra, 2011 In this work, we give two characterisations of the general linear group as a group $G$ of finite Morley rank acting on an abelian connected group $V$ of finite Morley rank definably, faithfully and irreducibly. To be more precise, we prove that if the pseudoreflection rank of $G$ is equal to the Morley rank of $V$, then $V$ has a vector space structure
Ayşe Berkman, Alexandre Borovik
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Linear representations of soluble groups of finite Morley rank [PDF]
Proceedings of the American Mathematical Society, 2010 Sufficient conditions are given for groups of finite Morley rank having nontrivial torsion-free nilpotent normal subgroups to have linear representations with small kernels. In particular, centreless connected soluble groups of finite Morley rank with torsion-free Fitting subgroups have faithful linear representations.
Tuna Altınel, John S. Wilson
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Permutation groups of finite Morley rank [PDF]
, 2007 The paper bounds the Morley rank of a definably primitive permutation group of finite Morley rank in terms of the rank of the set on which it acts.
A. Borovik, G. Cherlin
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On 2-step solvable groups of finite Morley rank [PDF]
Proceedings of the American Mathematical Society, 1990 We prove the following results: Theorem 1. Let G G be a connected, centerless, solvable group of class 2 and of finite Morley rank. Then we can interpret in G G finitely many connected, solvable of class 2 and centerless algebraic groups G ~
Kathryn Enochs, Ali Nesin
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CIT Groups of Finite Morley Rank (II)
Journal of Algebra, 1994 [This review concerns also the two preceding items Zbl 0818.20029 and Zbl 0818.20030.] An \(\omega\)-stable group of finite Morley rank (a group of finite rank, for short) is a group whose first order theory is \(\omega\)-stable of finite Morley rank. (For the latter model theoretic notion, see e.g. \textit{A.
A. Borovik, Ali Nesin
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UNIVERSAL COVERS OF COMMUTATIVE FINITE MORLEY RANK GROUPS [PDF]
Journal of the Institute of Mathematics of Jussieu, 2018 We give an algebraic description of the structure of the analytic universal cover of a complex abelian variety which suffices to determine the structure up to isomorphism. More generally, we classify the models of theories of ‘universal covers’ of rigid divisible commutative finite Morley rank groups.
Martin Bays, Bradd Hart, Anand Pillay
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