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

Mathematics

Hossein Moradi¹  Ali Iranmanesh¹  MohammadReza Darafsheh² 

[1] Department of Mathematics, Tarbiat Modares University, P.O. Box 14115-137, Tehran, Iran;School of mathematics, statistics and computer, College of science, University of Tehran, P.O. Box 14155-6455, Tehran, Iran;

关键词: prime graph;    simple group;    orthogonal groups;    quasirecognition;   

DOI  :  10.3390/math6040057

来源: DOAJ

【 摘 要 】

Let G be a finite group. The prime graphΓ ( G )of G is defined as follows: The set of vertices ofΓ ( G )is the set of prime divisors of| G |and two distinct vertices p andp ′are connected inΓ ( G ), whenever G contains an element of orderpp ′ . A non-abelian simple group P is called recognizable by prime graph if for any finite group G withΓ ( G ) = Γ ( P ), G has a composition factor isomorphic to P. It is been proved that finite simple groups2 D n ( q ) , wheren ≠ 4 k, are quasirecognizable by prime graph. Now in this paper we discuss the quasirecognizability by prime graph of the simple groups2 D2 k( q ) , wherek ≥ 9and q is a prime power less than10 5.

【 授权许可】

Unknown