On quasirecognition by prime graph of the simple groups $A^{+}_{n}(p)$ and $A^{-}_{n}(p)$

Abstract

Let p be prime and n be a natural number. In this paper, we present two conditions such that if p and n satisfy these conditions, then the simple groups [Formula: see text] and [Formula: see text] are quasirecognizable by prime graph and also quasirecognizable by spectrum. One of these conditions has a relation with Artin's Conjecture. As an application, we see that for every p < 1000, there exists a natural number m, such that for all n ≥ m, the simple groups [Formula: see text] and [Formula: see text] are quasirecognizable by prime graph.