Groups of Finite Morley Rank with Solvable Local Subgroups

Adrien Deloro (1) , Eric Jaligot (2)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
2 IF - Institut Fourier

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 a main Uniqueness Theorem, analogous to the Bender method in finite group theory, and derive its corollaries. We also consider homogeneous cases and study torsion.

Mots clés: Cherlin-Zilber Conjecture; Morley Rank; Feit-Thompson Theorem; Bender Method

Domaines: Théorie des groupes [math.GR]; Logique [math.LO]

Adrien Deloro, Eric Jaligot. Groups of Finite Morley Rank with Solvable Local Subgroups. Communications in Algebra, 2012, 40 (3), pp.1019-1068. ⟨10.1080/00927872.2010.544695⟩. ⟨hal-00250070v4⟩