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

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

*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

## Subject

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