Recognition of the projective special linear group over GF(3).

Let P be a finite group and denote by ω( P) the set of its element orders. P is called κ-recognizable by the set of its element orders if for any finte group G with ω( G) = ω( P) there are, up to isomorphism, κ finite groups G such that G ≃ P. In this paper we will prove that the group L _p(3), where p > 3 is a prime number, is at most 2-recognizable. [ABSTRACT FROM AUTHOR]