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.

Quasirecognition by Prime Graph of the Groups 2D2n(q) Where q < 105

“…Quasirecognizability by prime graph of groups G 2 (3 2n+1 ) and 2 B 2 (2 2n+1 ) has been proved in [4]. In [5][6][7], finite groups with the same prime graphs as Γ [8], it is proved that if p is a prime less than 1000, for suitable n, the finite simple groups L n (p) and U n (p) are quasirecognizable by prime graph. Now as the main result of this paper, we prove the following theorem:…”

Quasirecognition by Prime Graph of the Groups ²<em>D</em>_2<em>n</em>(<em>q</em>) Where <em>q</em> &lt; 10⁵

“…In [7,8,9] finite groups with the same prime graph as Γ(L n (2)), Γ(U n (2)), Γ(D n (2)), Γ( 2 D n (2)) and Γ( 2 D 2k (3)) are obtained. Also in [10] it is proved that if p is a prime less than 1000 and for suitable n, the finite sinple groups L n (p), U n (p) are quasirecognizable by prime graph. Now as the main result of this paper, we prove the following theorem:…”