Learn More
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)
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)
  • 1