Extensions of unirational groups

Abstract We undertake a study of extensions of unirational algebraic groups. We prove that extensions of unirational groups are also unirational over fields of degree of imperfection 1, but that this fails over every field of higher degree of imperfection, answering a question of Achet. We also initiate a study of those groups which admit filtrations with unirational graded pieces, and show that one may deduce unirationality of unipotent groups from unirationality of certain quotients.