Results 1 to 10 of about 164 (123)

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
doaj   +3 more sources

Groups of finite Morley rank with a pseudoreflection action

Journal of Algebra, 2012
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
Alexandre Borovik
exaly   +3 more sources

The Bender method in groups of finite Morley rank

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
exaly   +5 more sources

Signalizers and balance in groups of finite Morley rank

Journal of Algebra, 2009
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
exaly   +3 more sources

Small groups of finite Morley rank with involutions [PDF]

Journal Fur Die Reine Und Angewandte Mathematik, 2010
We consider groups of finite Morley rank with solvable local subgroups of even and mixed types. We also consider miscellaneous aspects of small groups of finite Morley rank of odd type.
Adrien Deloro, Eric Jaligot
exaly   +4 more sources

Solvable groups of finite Morley rank

Journal of Algebra, 1989
This paper is an important contribution toward Cherlin's conjecture. This conjecture states that a simple group of finite Morley rank is an algebraic group over an algebraically closed field. In fact, there are many results proving that the groups of finite Morley rank look very much like algebraic groups over an algebraically closed field, and the ...
Ali Nesin
exaly   +2 more sources

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, Eric Jaligot
exaly   +3 more sources

On groups of finite Morley rank with a split BN-pair of rank 1

Journal of Algebra, 2011
This work relates to groups of finite Morley rank and the Cherlin-Zilber ``algebraicity'' conjecture that infinite simple such groups are algebraic. The approach involves Moufang sets. The paper focuses on the case where the group is assumed to have a split BN-pair of Tits rank 1, as bigger ranks are investigated by \textit{L. Kramer}, \textit{K. Tent},
exaly   +2 more sources

SEMISIMPLE TORSION IN GROUPS OF FINITE MORLEY RANK [PDF]

Journal of Mathematical Logic, 2009
We prove several results about groups of finite Morley rank without unipotent p-torsion: p-torsion always occurs inside tori, Sylow p-subgroups are conjugate, and p is not the minimal prime divisor of our approximation to the "Weyl group". These results are quickly finding extensive applications within the classification project.
Jeffrey Burdges, Gregory L. Cherlin
openaire   +3 more sources

A GENERATION THEOREM FOR GROUPS OF FINITE MORLEY RANK [PDF]

Journal of Mathematical Logic, 2008
We deal with two forms of the "uniqueness cases" in the classification of large simple K*-groups of finite Morley rank of odd type, where large means the 2-rank m2(G) is at least three. This substantially extends results known for even larger groups having Prüfer 2-rank at least three, so as to cover the two groups PSp4and G2.
Jeffrey Burdges, Gregory L. Cherlin
openaire   +2 more sources