On the restriction of characters of special linear groups of dimension three. (Q553435)

Let \(G=\text{SL}(3,q)\) where \(q>2\) is a power of a prime \(p\). It was shown by \textit{E. Güzel} [J. Karadeniz Tech. Univ., Fac. Arts Sci., Ser. Math.-Phys. 11, 53-62 (1988; Zbl 0745.20037)] that for every irreducible character \(\chi\) of \(G\), the restriction \(\chi_P\) to a Sylow \(p\)-subgroup \(P\) has a constituent of degree \(1\) and multiplicity \(1\). This paper provides an alternative proof. The author's interest in this question arises from an application of the result to construction of matrix representations of arbitrary finite groups [see \textit{V. Dabbaghian-Abdoly}, Can. J. Math. 58, No. 1, 23-38 (2006; Zbl 1096.20017)].