Clifford correspondences and irreducible restrictions of characters

TL;DR

This paper investigates the relationships between characters of finite groups and their normal subgroups, providing new theorems about Clifford correspondences for irreducible restrictions.

Contribution

It introduces a new theorem linking Clifford correspondences to irreducible restrictions of characters in finite groups.

Findings

Established a theorem on Clifford correspondences for irreducible restrictions

Clarified the structure of characters inducing irreducible restrictions

Enhanced understanding of character restrictions in finite group theory

Abstract

For a finite group $G$ and complex character $\chi\in\mathrm{Irr}(G)$ that restricts irreducibly to a normal subgroup $N\vartriangleleft G,$ we prove a theorem about Clifford correspondences between the characters of subgroups of $G$ that induce $\chi.$