  NTP2 is a large class of first-order theories defined by Shelah and
generalizing simple and NIP theories. Algebraic examples of NTP2 structures are
given by ultra-products of p-adics and certain valued difference fields (such
as a non-standard Frobenius automorphism living on an algebraically closed
valued field of characteristic 0). In this note we present some results on
groups and fields definable in NTP2 structures. Most importantly, we isolate a
chain condition for definable normal subgroups and use it to show that any NTP2
field has only finitely many Artin-Schreier extensions. We also discuss a
stronger chain condition coming from imposing bounds on burden of the theory
(an appropriate analogue of weight), and show that every strongly dependent
valued field is Kaplansky.
