Some formulas for conjugation (Q2782157)

This paper gives two formulae concerned, it claims, with the conjugation in the odd primary Steenrod algebra and its dual. In reality the formulae deal with an operation \(X \mapsto \widehat{X}\) whose connection with the conjugation is never adequately explained. Previous authors have used a convention where \(\widehat{X} = \pm \chi(X)\), but such a simple relation does not agree with certain formulae in the paper under review (such as those in the proof of Lemma 3.1). In fact this reviewer has been unable to discover a relation between \(\widehat{X}\) and \(\chi(X)\) for which all the formulae in the paper are true. Nevertheless, at least one interpretation of Theorem 1.1 of the paper is correct, as it is subsumed in a result of \textit{D. M. Meyer} [Homology Homotopy Appl. 2, 1-16 (2000; Zbl 0947.55018)].