Model theoretic connected components of groups

We give a general exposition of model theoretic connected components of groups. We show that if a group G has NIP, then there exists the smallest invariant (over some small set) subgroup of G with bounded index (Theorem 5.3). This result extends a theorem of Shelah from [21] . We consider also in th...

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Veröffentlicht in:	Israel journal of mathematics 2011-08, Vol.184 (1), p.251-274
1. Verfasser:	Gismatullin, Jakub
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Analysis Applications of Mathematics Group Theory and Generalizations Mathematical and Computational Physics Mathematics Mathematics and Statistics Theoretical
Online-Zugang:	Volltext
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Zusammenfassung:	We give a general exposition of model theoretic connected components of groups. We show that if a group G has NIP, then there exists the smallest invariant (over some small set) subgroup of G with bounded index (Theorem 5.3). This result extends a theorem of Shelah from [21] . We consider also in this context the multiplicative and the additive groups of some rings (including infinite fields).
ISSN:	0021-2172 1565-8511
DOI:	10.1007/s11856-011-0067-8