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The Structure of an SL 2 ‐module of finite Morley rank
Author(s) -
Tindzogho Ntsiri Jules
Publication year - 2017
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201600021
Subject(s) - mathematics , rank (graph theory) , abelian group , combinatorics , torus , rank of an abelian group , order (exchange) , group (periodic table) , action (physics) , elementary abelian group , pure mathematics , discrete mathematics , physics , geometry , finance , quantum mechanics , economics
We consider a universe of finite Morley rank and the following definable objects: a field K , a non‐trivial action of a group G ≅ SL 2 ( K )on a connected abelian group V , and a torus T of G such thatC V ( T ) = 0 . We prove that every T ‐minimal subgroup of V has Morley rankrk ( K ) . Moreover V is a direct sum ofN G ( T ) ‐minimal subgroups of the form W ⊕ W ζ , where W is T ‐minimal and ζ is an element of G of order 4 inverting T .