On quasirecognition by prime graph of the simple groups A(n)(+) (p) and A(n)(-) (p)

摘要

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 A(n)(+) (p) and A(n)(-) (p) 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 A(n)(+) (p) and A(n)-(p) are quasirecognizable by prime graph.