Measurable groups of low dimension | Zendy

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Measurable groups of low dimension

Author(s) -

Elwes Richard,

Ryten Mark

Publication year - 2008

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.200710052

Subject(s) - mathematics , unimodular matrix , abelian group , rank (graph theory) , group (periodic table) , dimension (graph theory) , infinity , pure mathematics , classification of finite simple groups , rank of an abelian group , interpretation (philosophy) , combinatorics , elementary abelian group , group theory , mathematical analysis , group of lie type , physics , quantum mechanics , computer science , programming language

We consider low‐dimensional groups and group‐actions that are definable in a supersimple theory of finite rank. We show that any rank 1 unimodular group is (finite‐by‐Abelian)‐by‐finite, and that any 2‐dimensional asymptotic group is soluble‐by‐finite. We obtain a field‐interpretation theorem for certain measurable groups, and give an analysis of minimal normal subgroups and socles in groups definable in a supersimple theory of finite rank where infinity is definable. We prove a primitivity theorem for measurable group actions. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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