A remark on unipotent groups of characteristic p>0

Abstract

Borel and Springer [1] deal with a unipotent group U defined over a field of prime characteristic p and investigate the conditions of the existence of the one dimensional subgroup to which a given element of the Lie algebra L(U) of U is tangent. They use the lemma (9. 15) (ii) (p. 493) in the proof of the last theorem (9. 16) (ii) (p. 495). In this report we shall show that this lemma is not correct (cf. §2). But a modification of it does not disturb the truth of the theorem. Moreover we want to show that the theorem (9. 16) (iii) in [1] is still true under a weaker assumption (cf. § 1). The notations in this report are the same as in [1].