0000000000243885

AUTHOR

Maria Loukaki

showing 2 related works from this author

On the number of constituents of products of characters

2022

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 ≥ 5, is bigger than (p + 1)/2, then it is at least p. We give a counterexample to this conjecture.

Discrete mathematicsAlgebra and Number TheoryConjectureApplied MathematicsProduct (mathematics)FOS: MathematicsGroup Theory (math.GR)Mathematics::Representation TheoryMathematics - Group TheoryCounterexampleMathematics
researchProduct

Homogeneous products of characters

2004

I. M. Isaacs has conjectured (see \cite{isa00}) that if the product of two faithful irreducible characters of a solvable group is irreducible, then the group is cyclic. In this paper we prove a special case of the following conjecture, which generalizes Isaacs conjecture. Suppose that $G$ is solvable and that $\psi,\phi\in\Irr(G)$ are faithful. If $\psi \phi=m\chi$ where $m$ is a positive integer and $\chi \in \Irr(G)$ then $\psi$ and $\phi$ vanish on $G- Z(G)$. In particular we prove that the above conjecture holds for $p$-groups.

CombinatoricsConjectureAlgebra and Number TheoryIntegerGroup (mathematics)Solvable groupHomogeneousProduct (mathematics)FOS: MathematicsGroup Theory (math.GR)Mathematics::Representation TheoryMathematics - Group TheoryMathematics
researchProduct