Quasirecognition by prime graph of L10(2)

Let G be a finite group. The prime graph of G is denoted by Γ(G). The main result we prove is as follows: If G is a finite group such that Γ(G) = Γ(L ₁₀(2)) then G/O ₂(G) is isomorphic to L ₁₀(2). In fact we obtain the first example of a finite group with the connected prime graph which is quasirecognizable by its prime graph. As a consequence of this result we can give a new proof for the fact that the simple group L ₁₀(2) is uniquely determined by the set of its element orders.