  We introduce the class of permawound unipotent groups, and show that they
simultaneously satisfy certain "ubiquity" and "rigidity" properties that in
combination render them very useful in the study of general wound unipotent
groups. As an illustration of their utility, we present two applications: We
prove that nonsplit smooth unipotent groups over (infinite) finitely-generated
fields have infinite first cohomology; and we show that every commutative
p-torsion wound unipotent group over a field of degree of imperfection 1 is the
maximal unipotent quotient of a commutative pseudo-reductive group, thus
partially answering a question of Totaro.
