Complex group algebras of almost simple groups with socle PS L n ( q ).

LetHbe a finite group,n≥3, andqbe a prime power such thatq−1 divides neithernnorn−1. Denote byX1(H) the first column of the ordinary character table ofH. LetGbe a finite group such that. In this paper, we will show that if, thenH≅G. As a consequence, we show that the almost simple groupsGare 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. [ABSTRACT FROM AUTHOR]