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# Quasirecognition by Prime Graph of the Groups ^{2}*D*_{2n}(*q*) Where *q* < 10^{5}

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 ^{2}*D*_{2n}(*q*) Where *q* < 10^{5}. *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 < 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^{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*_{2k}(*q*), where*k*≥ 9 and*q*is a prime power less than 10^{5}.## Keywords

prime graph; simple group; orthogonal groups; quasirecognition

## Subject

MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory

Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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