arXiv subjects
Publications and source records attributed to Edith Adan-Bante.
Let p be a prime number. Let G be a finite p-group and $χ\in Irr(G)$. Denote by $\barχ \in Irr(G)$ the complex conjugate of $χ$. Assume that $χ(1)=p^n$. We show that the number of distinct irreducible constituents of the product $χ\barχ$ is at least $2n(p-1)+1$.
Let G be a finite solvable group and $χ\in \Irr(G)$ be a faithful character. We show that the derived length of G is bounded by a linear function of the number of distinct irreducible constituents of $χ\barχ$. We also discuss other properties of the decomposition of $χ\barχ$ into its irreducible constituents.