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Groups in supersimple and pseudofinite theories
Author(s) -
Elwes Richard,
Jaligot Eric,
Macpherson Dugald,
Ryten Mark
Publication year - 2011
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/pdr002
Subject(s) - mathematics , rank (graph theory) , set (abstract data type) , combinatorics , action (physics) , pure mathematics , computer science , physics , quantum mechanics , programming language
We consider groups G interpretable in a supersimple finite rank theory T such that T eq eliminates ∃ ∞ . It is shown that G has a definable soluble radical. If G has rank 2, then if G is pseudofinite, it is soluble‐by‐finite, and partial results are obtained under weaker hypotheses, such as ‘functional unimodularity’ of the theory. A classification is obtained when T is pseudofinite and G has a definable and definably primitive action on a rank 1 set.