Character expansiveness in finite groups

We say that a finite group G is conjugacy expansive if for any normal subset S and any conjugacy class C of G the normal set SC consists of at least as many conjugacy classes of G as S does. Halasi, Mar\'oti, Sidki, Bezerra have shown that a group is conjugacy expansive if and only if it is a direct product of conjugacy expansive simple or abelian groups. By considering a character analogue of the above, we say that a finite group G is character expansive if for any complex character \alpha and irreducible character \chi of G the character \alpha \chi has at least as many irreducible constituents, counting without multiplicity, as \alpha does. In this paper we take some initial steps in determining character expansive groups.

Keywords:

Finite group , Irreducible characters , product of characters