On commutative $p$-schemes of order $p^4$

TL;DR

This paper investigates the existence and schurity of commutative p-schemes of order p^4, providing conditions under which these schemes are schurian using the concepts of thin radical and residue.

Contribution

It offers new sufficient conditions for the schurity of commutative p-schemes of order p^4 based on structural properties.

Findings

Sufficient conditions for schurity of p-schemes of order p^4

Use of thin radical and residue in analysis

Open questions related to the results

Abstract

In this article, we consider the existence and schurity problem on commutative $p$-schemes of order $p^4$. Using the thin radical and thin residue, we give sufficient conditions for such $p$-schemes to be schurian. We also give questions related to our results.