Results 101 to 110 of about 164 (123)

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.
openaire   +2 more sources

Groups of Finite Morley Rank

1994
Abstract The book is devoted to the theory of groups of finite Morley rank. These groups arise in model theory and generalize the concept of algebraic groups over algebraically closed fields. The book contains almost all the known results in the subject. Trying to attract pure group theorists in the subject and to prepare the graduate
Alexandre Borovik, Ali Nesin
openaire   +1 more source

The geometry of forking and groups of finite Morley rank

Journal of Symbolic Logic, 1995
AbstractThe notion of CM-triviality was introduced by Hrushovski, who showed that his new strongly minimal sets have this property. Recently Baudisch has shown that his new ω1-categorical group has this property. Here we show that any group of finite Morley rank definable in a CM-trivial theory is nilpotent-by-finite, or equivalently no simple group of
openaire   +2 more sources

A GENERIC IDENTIFICATION THEOREM FOR GROUPS OF FINITE MORLEY RANK

Journal of the London Mathematical Society, 2004
The paper is a contribution to the classification of infinite simple groups of finite Morley rank, and so to the solution of the classical conjecture of Cherlin and Zilber saying that such a group is a simple algebraic group over an algebraically closed field. The analysis of a possible minimal counterexample \(G\) to this conjecture is usually divided
Berkman, Ayşe, Borovik, Alexandre V.; id_orcid 0000-0003-0808-8687   +1 more
openaire   +2 more sources

Groups of finite Morley rank with transitive group automorphisms

Journal of Symbolic Logic, 1989
The aim of this short note is to prove the following result:Theorem. Let G be a group of finite Morley rank with Aut G acting transitively on G/{1}. Then G is either abelian or a bad group.Bad groups were first defined by Cherlin [Ch]: these are groups of finite Morley rank without solvable and nonnilpotent connected subgroups.
openaire   +1 more source

The existence of Carter subgroups in groups of finite Morley rank

Journal of Group Theory, 2005
The authors show that any group of finite Morley rank contains a Carter subgroup, i.e. a definable connected nilpotent subgroup of finite index in its normalizer. This partially generalizes earlier results of \textit{O. Frécon} [J. Algebra 229, No. 1, 118-152 (2000; Zbl 0984.20022)] and \textit{F. O. Wagner} [Arch. Math. Logic 33, No.
Frécon, Olivier, Jaligot, Eric
openaire   +1 more source

On the Schur-Zassenhaus theorem for groups of finite Morley rank

Journal of Symbolic Logic, 1992
The Schur-Zassenhaus Theorem is one of the fundamental theorems of finite group theory. Here is its statement:Fact1.1 (Schur-Zassenhaus Theorem). Let G be a finite group and let N be a normal subgroup of G. Assume that the order ∣N∣ is relatively prime to the index [G:N].
Alexandre V. Borovik, Ali Nesin
openaire   +2 more sources

Generalized Fitting subgroup of a group of finite Morley rank

Journal of Symbolic Logic, 1991
AbstractWe define a characteristic and definable subgroup F*(G) of any group G of finite Morley rank that behaves very much like the generalized Fitting subgroup of a finite group. We also prove that semisimple subnormal subgroups of G are all definable and that there are finitely many of them.
openaire   +2 more sources

Carter subgroups in tame groups of finite Morley rank

jgth, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

Fusion of 2-elements in groups of finite Morley rank

Journal of Symbolic Logic, 2001
The Alperin-Goldschmidt Fusion Theorem [1, 5], when combined with pushing up [7], was a useful tool in the classification of the finite simple groups. Similar theorems are needed in the study of simple groups of finite Morley rank, in the even type case (that is, when the Sylow 2-subgroups are of bounded exponent, as in algebraic groups over fields of ...
openaire   +2 more sources