Complex group algebras of almost simple groups with socle PSLn(q)

Let H be a finite group, n >= 3, and q be a prime bower such that q - 1 divides neither n nor n -1, Denote by X-1 (H) the first column of the ordinary character table of H. Let G be a finite group such that PSLn- (q) <= G <= PGL(n)(q). In this paper, we will show that if X-1 (H) = X-1 (G), then H congruent to G. As a consequence' we show that the almost simple groups,G are uniquely determined by the structure of their complex group algebras. This extends a result of Tong -Viet [30] to a family of almost simple groups of Lie type of arbitrary rank