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Primitive Permutation Groups of Finite Morley Rank
Author(s) -
Macpherson Dugald,
Pillay Anand
Publication year - 1995
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-70.3.481
Subject(s) - mathematics , rank (graph theory) , permutation (music) , combinatorics , permutation group , pure mathematics , physics , acoustics
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 , +,.).