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THE ELLIS GROUP CONJECTURE AND VARIANTS OF DEFINABLE AMENABILITY

Published online by Cambridge University Press:  21 December 2018

GRZEGORZ JAGIELLA
GRZEGORZ JAGIELLA*
Affiliation:
INSTYTUT MATEMATYCZNY UNIWERSYTETU WROCŁAWSKIEGOPL. GRUNWALDZKI 2/4 50-384WROCŁAW, POLANDE-mail: [email protected]
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Abstract

We consider definable topological dynamics for NIP groups admitting certain decompositions in terms of specific classes of definably amenable groups. For such a group, we find a description of the Ellis group of its universal definable flow. This description shows that the Ellis group is of bounded size. Under additional assumptions, it is shown to be independent of the model, proving a conjecture proposed by Newelski. Finally we apply the results to new classes of groups definable in o-minimal structures, generalizing all of the previous results for this setting.

Keywords

Primary 03C9954H20Secondary 03C64definable topological dynamicsdefinable amenabilityo-minimality
Type
Articles
Information
The Journal of Symbolic Logic , Volume 83 , Issue 4 , December 2018 , pp. 1376 - 1390
Copyright
Copyright © The Association for Symbolic Logic 2018 

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