International audienceWe 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

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Suite de la réécriture de [Gregory Cherlin, Eric Jaligot, Tame minimal simple groups of finite Morley rank, J. Algebra 276 (1) (2004) 13-79] commencée dans [Adrien Deloro, Groupes simples connexes minimaux algébriques de type impair, J. Algebra 317 (2) (2007) 877-923]. Nous nous intéressons à d'éventuels contre-exemples à la conjecture de Cherlin-Zilber, à savoir des groupes simples connexes minimaux qui ne soient pas algébriques. Nous en limitons la structure en type impair.

We classify actions of groups of finite Morley rank on abelian groups of Morley rank 2: there are essentially two, namely the natural actions of SL(V) and GL(V) with V a vector space of dimension 2. We also prove an identification theorem for the natural module of SL2 in the finite Morley rank category.

avea lasciati scemi di sé, Virgilio dolcissimo patre, Virgilio a cui per mia salute die' mi.Abstract. We classify a large class of small groups of finite Morley rank: N • • -groups which are the infinite analogues of Thompson's N -groups. More precisely, we constrain the 2-structure of groups of finite Morley rank containing a definable, normal, nonsoluble, N • • -subgroup.