Products of characters with few irreducible constituents

TL;DR

This paper investigates certain solvable groups with irreducible characters whose products have at most two non-principal irreducible constituents, revealing structural properties of these groups.

Contribution

It characterizes solvable groups with irreducible characters whose products have limited irreducible constituents, advancing understanding of character product structures.

Findings

Identifies conditions for solvable groups with specific character product properties

Classifies groups based on the number of irreducible constituents in character products

Provides structural insights into groups with constrained character product decompositions

Abstract

We study the solvable groups $G$ that have an irreducible character $\chi\in \Irr(G)$ such that $\chi \bar{\chi}$ has at most two non-principal irreducible constituents.