Groups in supersimple and pseudofinite theories | Zendy

Elwes Richard | Zendy; Jaligot Eric | Zendy; Macpherson Dugald | Zendy; Ryten Mark | Zendy

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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.

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