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

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 contains an element of order p p ′ . 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. It is been proved that finite simple groups 2 D n ( q ) , where n ≠ 4 k , are quasirecognizable by prime graph. Now in this paper we discuss the quasirecognizability by prime graph of the simple groups 2 D 2 k ( q ) , where k ≥ 9 and q is a prime power less than 10 5 .

Keywords

• prime graph
• simple group
• orthogonal groups
• quasirecognition