Abstract
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).
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The author is supported by the Polish Goverment MNiSW grant N N201 384134.
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Gismatullin, J. Model theoretic connected components of groups. Isr. J. Math. 184, 251–274 (2011). https://doi.org/10.1007/s11856-011-0067-8
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DOI: https://doi.org/10.1007/s11856-011-0067-8