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arXiv · 0707.0137

Model theoretic connected components of groups

Jakub Gismatullin
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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 theorem of Shelah. We consider also in this context the multiplicative and the additive groups of some rings (including infite fields).

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Jakub Gismatullin. 2010-02-09. Model theoretic connected components of groups. https://arxiv.org/abs/0707.0137

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