Results 21 to 30 of about 6,390 (190)
Conjugacy of Carter Subgroups in Groups of finite Morley Rank [PDF]
Journal of Mathematical Logic, 2008 The Cherlin–Zil'ber Conjecture states that all simple groups of finite Morley rank are algebraic. We prove that any minimal counterexample to this conjecture has a unique conjugacy class of Carter subgroups, which are analogous to Cartan subgroups in algebraic groups.
Olivier Frécon
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Unipotence in positive characteristic for groups of finite Morley rank
Turkish Journal of Mathematics, 2023 : In this article we define a new form of unipotence in groups of finite Morley rank which extends Burdges unipotence to any characteristic. In particular, we show that every connected solvable group of finite Morley rank G has a definable connected subgroup
Jules Tindzogho Ntsiri
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Splitting in solvable groups of finite Morley rank
Journal of Logic and Analysis, 2010 We exhibit counterexamples to a Conjecture of Nesin, since we build a connected solvable group with finite center and of finite Morley rank in which no normal nilpotent subgroup has a nilpotent complement. The main result says that each centerless connected solvable group G of finite Morley has a normal nilpotent subgroup U and an abelian subgroup T ...
Olivier Frécon
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Automorphism groups of small simple groups of finite Morley rank [PDF]
Proceedings of the American Mathematical Society, 2010 IfGGis a minimal connected simple group of finite Morley rank with a nontrivial Weyl group, then its connected definable automorphism groups are inner.
Olivier Frécon
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Groups of Finite Morley Rank with Solvable Local Subgroups [PDF]
Communications in Algebra, 2012 We lay down the fundations of the theory of groups of finite Morley rank in which local subgroups are solvable and we proceed to the local analysis of these groups. We prove the main Uniqueness Theorem, analogous to the Bender method in finite group theory, and derive its corollaries. We also consider homogeneous cases as well as torsion.
Adrien Deloro, Éric Jaligot
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On Weyl groups in minimal simple groups of finite Morley rank [PDF]
Israel Journal of Mathematics, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
T. Altinel +2 more
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Uniqueness cases in odd‐type groups of finite Morley rank [PDF]
, 2007 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.
A. Borovik, Jeffrey Burdges, Ali Nesin
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Signalizers and balance in groups of finite Morley rank [PDF]
Journal of Algebra, 2007 We show that a minimal counter example to the Cherlin-Zilber Algebraicity Conjecture for simple groups of finite Morley rank has Prufer 2-rank at most two. This article covers the signalizer functor theory and identifies the groups of Lie rank at least three; leaving the uniqueness case analysis to previous articles.
Jeffrey Burdges
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Tame minimal simple groups of finite Morley rank
Journal of Algebra, 2004 The paper is a contribution to the program aiming to prove the Cherlin-Zil'ber algebraicity conjecture: any infinite simple group of finite Morley rank is an algebraic group over an algebraically closed field. A group of finite Morley rank is said to be tame if does not interpret a bad field naturally.
G. Cherlin, E. Jaligot
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Groups of Finite Morley Rank with Strongly Embedded Subgroups
Journal of Algebra, 1996 The paper deals with the Cherlin-Zil'ber conjecture, the central problem in the area of groups of finite Morley rank. (The state of the art has been presented in the book of \textit{A. Borovik} and \textit{A. Nesin} [Groups of finite Morley rank, Clarendon Press, Oxford (1994; Zbl 0816.20001)].) The conjecture states that any infinite simple group of ...
T. Altinel
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