On the anti-automorphism of the Steenrod algebra: II

TL;DR

This paper investigates the structure of the Steenrod algebra, demonstrating that Barratt and Miller's relations encompass all relations among specific elements, and provides a minimal set of these relations.

Contribution

It shows that Barratt and Miller's relations include all relations among certain Steenrod algebra elements and identifies a minimal set of these relations.

Findings

All relations among P^i χ P^{n-i} are included in Barratt and Miller's relations.

A minimal set of relations among these elements is established.

The results clarify the algebraic structure of the Steenrod algebra.

Abstract

The relations of Barratt and Miller are shown to include all relations among the elements $P^i\chi P^{n-i}$ in the mod $p$ Steenrod algebra, and a minimal set of relations is given.