A note on quasi-elementary sub-Hopf algebras of the polynomial part of the odd primary Steenrod algebra

TL;DR

This paper proves that all quasi-elementary sub-Hopf algebras of the polynomial part of the odd primary Steenrod algebra are contained within a specific sub-Hopf algebra called D.

Contribution

It establishes a structural restriction on quasi-elementary sub-Hopf algebras within the polynomial part of the odd primary Steenrod algebra.

Findings

All quasi-elementary sub-Hopf algebras are contained in D.

Provides insight into the algebraic structure of the Steenrod algebra.

Clarifies the placement of sub-Hopf algebras in the polynomial part.

Abstract

We prove that every quasi-elementary sub-Hopf algebra of the polynomial part of the odd primary Steenrod algebra must lie in a certain sub-Hopf algebra called $D$.