Stripping and conjugation in the mod $p$ Steenrod algebra and its dual

Abstract

Let $p$ be an odd prime and ${\cal A}^{\ast}$ the mod $p$ Steenrod algebra. We study the technique known as "stripping'' applied to ${\cal A}^{\ast}$ and derive certain conjugation formulas both for ${\cal A}^{\ast}$ and its dual, generalising work of J. H. Silverman for $p=2$ ("Conjugation and excess in the Steenrod algebra", Proc. Am. Math. Soc. 119 (1993), no. 2, 657-661; "Hit polynomials and conjugation in the dual Steenrod algebra", Math. Proc. Camb. Philos. Soc. 123 (1998), no. 531-547) to the case of an odd prime.