On the number of constituents of products of characters

TL;DR

This paper challenges a conjecture in character theory of finite p-groups by providing a counterexample that refutes the proposed lower bound on the number of irreducible constituents in character products.

Contribution

The paper presents a counterexample to a longstanding conjecture about the minimum number of irreducible constituents in the product of two faithful irreducible characters of a finite p-group.

Findings

Counterexample disproves the conjecture for p ≥ 5

The minimal number of constituents can be less than (p+1)/2

The result refines understanding of character products in p-groups

Abstract

It has been conjectured that if the number of distinct irreducible constituents of the product of two faithful irreducible characters of a finite $p$-group, for $p\geq5$, is bigger than $(p+1)/2$, then it is at least $p$. We give a counterexample to this conjecture.