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

Abstract

Abstract. Let G be a finite group. The prime graph Γ(G) of G is defined as follows: The set of vertices of Γ(G) is the set of prime divisors of |G| and two distinct vertices p and p are connected in Γ(G), whenever G has an element of order pp . A non-abelian simple group P is called recognizable by prime graph if for any finite group G with Γ(G) = Γ(P ), G has a composition factor isomorphic to P . In [4] proved finite simple groups 2 D n (q), where n = 4k are quasirecognizable by prime graph. Now in this paper we discuss the quasirecognizability by prime graph of the simple groups 2 D 2k (q), where k ≥ 9 and q is a prime power less than 10 5 .