Minimal-order groups with an irreducible character of degree $p$ or $p^2$

TL;DR

This paper characterizes the smallest finite groups that have an irreducible complex character of degree either p or p^2, where p is a prime, providing a classification of such groups.

Contribution

It offers a complete characterization of minimal-order groups with an irreducible character of degree p or p^2, advancing the understanding of group representation structures.

Findings

Identifies all minimal groups with an irreducible character of degree p.

Identifies all minimal groups with an irreducible character of degree p^2.

Provides structural descriptions of these groups.

Abstract

We characterize the finite groups of minimal order that admit an irreducible complex character of degree $p$ or $p^2$, where $p$ is a prime.