On the Restriction of Characters of Special Linear Groups of Dimension Three

Let G be the special linear group SL(3, q), where q is power of a prime p. Here, we show that P has a linear constituent with multiplicity one for each irreducible character and Sylow p-subgroup P of G. Furthermore, if cf(G) is the vector space of class functions of G, we show that the restriction of a subset of irreducible characters of G on P is a basis for the vector space of class functions defined on P spanned by { Ø P | Ø in cf(G)}