Quasirecognition by Prime Graph of the Groups 2 D 2n ( q ) Where q < 10 5

Hossein Moradi, Mohammad Reza Darafsheh and Ali Iranmanesh
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Hossein Moradi: Department of Mathematics, Tarbiat Modares University, P.O. Box 14115-137, Tehran, Iran
Mohammad Reza Darafsheh: School of mathematics, statistics and computer, College of science, University of Tehran, P.O. Box 14155-6455, Tehran, Iran
Ali Iranmanesh: Department of Mathematics, Tarbiat Modares University, P.O. Box 14115-137, Tehran, Iran

Mathematics, 2018, vol. 6, issue 4, 1-6

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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