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, Maroti, 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 a and irreducible character x of G the character cxx has at least as many irreducible constituents, counting without multiplicity, as a does. In this paper we take some initial steps in determining character expansive groups.