Model theoretic connected components of groups

Details Model theoretic connected components of groups Model theoretic connected components of groups

2007-07-02

arxiv.org/abs/0707.0137v4

Mathematics

Logic

20 pages, corected, to appear in Israel J. of Math

Scientific paper

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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