Model theoretic connected components of groups
Logic
2010-02-09 v4 Group Theory
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).
Cite
@article{arxiv.0707.0137,
title = {Model theoretic connected components of groups},
author = {Jakub Gismatullin},
journal= {arXiv preprint arXiv:0707.0137},
year = {2010}
}
Comments
20 pages, corected, to appear in Israel J. of Math