Results 91 to 100 of about 164 (123)

Around unipotence in groups of finite Morley rank

Journal of Group Theory, 2006
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Olivier Frécon
exaly   +3 more sources

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
Anand Pillay
exaly   +3 more sources

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.
Gregory Cherlin
exaly   +2 more sources

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 ...
Hendrik Van Maldeghem, Linus Kramer, Katrin Tent   +2 more
exaly   +2 more sources

On CN-Groups of Finite Morley Rank

Journal of the London Mathematical Society, 1994
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DeBonis, Mark, Nesin, Ali
openaire   +2 more sources

Simple Groups of Finite Morley Rank

2008
The book gives a detailed presentation of the classification of the simple groups of finite Morley rank which contain a nontrivial unipotent 2-subgroup. They are linear algebraic groups over algebraically closed fields of characteristic 2. Although the story told in the book is inspired by the classification of the finite simple groups, it goes well ...
Altinel, Tuna, Borovik, Alexandre; id_orcid 0000-0003-0808-8687, Cherlin, Gregory   +2 more
openaire   +2 more sources

On Suzuki 2-groups of finite Morley rank

Journal of Group Theory, 2003
A Suzuki 2-group is defined to be a pair \((G,T)\), where \(G\) is a nilpotent 2-group of bounded exponent and \(T\) is an Abelian group that acts on \(G\) by automorphisms so that the action of \(T\) on the involutions of \(G\) is transitive. If, in addition, \(T\) acts on \(G\) freely, \((G,T)\) is called a free Suzuki 2-group.
Davis, MK, Nesin, A
openaire   +2 more sources