CHARACTER EXPANSIVENESS IN FINITE GROUPS

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