TY - JOUR
AU - Pillay, Anand
AB - We prove a version of the O'Nan–Scott Theorem for definably primitive permutation groups of finite Morley rank. This yields questions about structures of finite Morley rank of the form (F, +,., H) where (F, +,.) is an algebraically closed field and H is a central extension of a simple group with H ⩽ GL(n, F). We obtain partial results on such groups H, and show for example that if char(F) = 0, H is irreducible, and (in the sense for stable groups) some Borel subgroup of H is non‐abelian then H = Z(H). E where E ⩽ H is algebraic, that is, definable in (F, +,.).
TI - Primitive Permutation Groups of Finite Morley Rank
JF - Proceedings of the London Mathematical Society
DO - 10.1112/plms/s3-70.3.481
DA - 1995-05-01
UR - https://www.deepdyve.com/lp/wiley/primitive-permutation-groups-of-finite-morley-rank-M7T4EoTd4z
SP - 481
EP - 504
VL - s3-70
IS - 3
DP - DeepDyve
ER -