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- Olivier Frécon
- 2007

The Cherlin-Zil'ber Conjecture states that all simple groups of finite Morley rank are algebraic. We prove that any minimal counterexample to this conjecture has a unique conjugacy class of Carter subgroups, which are defined as being the definable connected nilpotent subgroups of finite index in their normalizers, and which are analogous to Cartan… (More)

We exhibit counterexamples to a Conjecture of Nesin, since we build a connected solvable group with finite center and of finite Morley rank in which no normal nilpotent subgroup has a nilpotent complement. The main result says that each centerless connected solvable group G of finite Morley has a normal nilpotent subgroup U and an abelian subgroup T such… (More)

- OLIVIER FRÉCON
- 2015

We consider an o-minimal expansion M 0 = (R 0 , <, +, · · ·) of a real closed field, and a real closed field R, complete in the sense of D. Scott, containing R 0 as a dense subfield. We show that M 0 has an elementary extension M = (R, <, +, · · ·) with domain R. Moreover, such a structure M with domain R is unique. Note In an unpublished article,… (More)

- OLIVIER FRÉCON
- 2013

We analyze the abstract structure of algebraic groups over an algebraically closed field K, using techniques from the theory of groups of finite Morley rank. For K of characteristic zero and G a given connected affine algebraic Q-group, the main theorem describes the algebraic structure of all the groups H(K) isomorphic as abstract groups to G(K), with H an… (More)

We study the structure of subgroups of minimal connected simple groups of finite Morley rank. We first establish a Jordan decomposition for a large family of minimal connected simple groups including those with a non-trivial Weyl group. We then show that definable, connected, solvable subgroups of such a simple group are the semi-direct product of their… (More)

- OLIVIER FRÉCON
- 2010

With any connected affine algebraic group G over an algebraically closed field K of characteristic zero, we associate another connected affine algebraic group D over K and a finite central subgroup F of D such that, up to isomorphism of algebraic groups, affine algebraic groups over K abstractly isomorphic to G are precisely of the form D/α(F)×K s + , where… (More)

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