Journal
ADVANCES IN MATHEMATICS
Volume 231, Issue 2, Pages 605-623Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aim.2012.05.022
Keywords
Definable group; o-minimality; Amenability; Bounded orbit
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Funding
- EPSRC [EP/I002294/1]
- Engineering and Physical Sciences Research Council [EP/I002294/1] Funding Source: researchfish
- EPSRC [EP/I002294/1] Funding Source: UKRI
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We give examples of definable groups G (in a saturated model, sometimes o-minimal) such that G(00) not equal G(000), yielding also new examples of non G-compact theories. We also prove that for G definable in a (saturated) o-minimal structure, G has a bounded orbit (i.e. there is a type of G whose stabilizer has bounded index) if and only if G is definably amenable, giving a positive answer to a conjecture of Newelski and Petrykowski in this special case of groups definable in o-minimal structures. (C) 2012 Elsevier Inc. All rights reserved.
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