Submission date: 15 May 2009.

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 5.4). This result extends theorem of Shelah. We consider also in this context the multiplicative and the additive groups of an infinite field.

Mathematics Subject Classification: 03C60; 20A15

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