CHARACTER EXPANSIVENESS IN FINITE GROUPS

Abstract. we say that a finite group g is conjugacy expansive if for any normal subset s and anyconjugacy class c of g the normal set sc consists of at least as many conjugacy classes of g as sdoes. halasi, maroti, sidki, bezerra have shown that a group is conjugacy expansive if and only if itis 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 expansiveif for any complex character ? and irreducible character x of g the character ?x has at least as manyirreducible constituents, counting without multiplicity, as ? does. in this paper we take some initialsteps in determining character expansive groups.