On n‐dependent groups and fields

First, an example of a 2‐dependent group without a minimal subgroup of bounded index is given. Second, all infinite n ‐dependent fields are shown to be Artin‐Schreier closed. Furthermore, the theory of any non separably closed PAC field has the IP n property for all natural numbers n and certain properties of dependent (NIP) valued fields extend to the n ‐dependent context.