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Preprint Number 1067

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1067. Bruno Poizat
Une minuscule amélioration du Théorème des Indécomposables

Submission date: 11 July 2016


We revise the hypothesis and the proof of Zilber's Indecomposability Theorem, for groups of finite Morley rank, following a version of this theorem by Wagner valid in the broader context of supersimple groups : it consists in attaching to any definable subset X of the group a definable subgroup e(X) which is easy to characterize (in the finite Morley rank case). We observe that old and new consequences of the theorem get a very smooth proof when we follow this new approach.

Mathematics Subject Classification:

Keywords and phrases: Groupes de rang de Morley fini, Théorème des Indécomposables, Conjecture d'Algébricité de Cherlin-Zilber, groupes finiment engendrés.

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