Preprint Article Version 1 This version is not peer-reviewed

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

Version 1 : Received: 7 July 2017 / Approved: 10 July 2017 / Online: 10 July 2017 (09:01:04 CEST)

How to cite: Moradi, H.; Darafsheh, M.R.; Iranmanesh, A. Quasirecognition by Prime Graph of the Groups 2D2n(q) Where q < 105. Preprints 2017, 2017070017 (doi: 10.20944/preprints201707.0017.v1). Moradi, H.; Darafsheh, M.R.; Iranmanesh, A. Quasirecognition by Prime Graph of the Groups 2D2n(q) Where q &lt; 105. Preprints 2017, 2017070017 (doi: 10.20944/preprints201707.0017.v1).

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 2Dn(q), where n ≠ 4k are quasirecognizable by prime graph. Now in this paper we discuss the quasirecognizability by prime graph of the simple groups 2D2k(q), where k ≥ 9 and q is a prime power less than 105.

Subject Areas

prime graph; simple group; orthogonal groups; quasirecognition

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