Let $G$ be a finite group. In [Ghasemabadi et al., characterizations of the simple group ${}^2D_n(3)$ by prime graph and spectrum, Monatsh Math., 2011] it is proved that if $n$ is odd, then ${}^2D _n(3)$ is recognizable by prime graph and also by element orders. In this paper we prove that if $n$ is even, then $D={}^2D_{n}(3)$ is quasirecognizable by prime graph, i.e. every finite group $G$ with $\Gamma(G)=\Gamma(D)$ has a unique nonabelian composition factor and this factor is isomorphic to $D$.

A. Babai and B. Khosravi (2011). Recognition by prime graph of $^2D_{2^m+1}(3)$. Sib. Math. J.. 52 (5), 788-795

2

A. Babai, B. Khosravi and N. Hasani (2009). Quasirecognition by prime graph of $^2D_p(3)$ where $p=2^n+1geq 5$
is a prime. Bull. Malays. Math. Sci. Soc. (2). 32 (3), 343-350

3

J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson (1985). Atlas of finite groups. Oxford University Press,
Oxford.

4

M. F. Ghasemabadi, A. Iranmanesh and N. Ahanjideh (2012). Characterizations of the simple group ${}^2D_n(3)$ by prime graph and spectrum. Monatsh Math.. 168 (3-4), 347-361

5

B. Khosravi, Z. Akhlaghi and M. Khatami (2011). Quasirecognition by prime graph of simple group $D_n(3)$. Publ. Math. Debrecen. 78 (2), 469-484

6

B. Khosravi and H. Moradi (2011). Quasirecognition by prime graph of finite simple groups $L_n(2)$ and $U_n(2)$. Acta Math. Hungar.. 132 (1-2), 140-153

7

B. Khosravi and H. Moradi (2012). Quasirecognition by prime graph of some orthogonal groups over the binary field. J. Algebra Appl.. 11 (3), 15-0

8

Z. Momen and B. Khosravi (2012). On $r$-recognition by prime graph of
$B_p(3)$ where $p$ is an odd prime. Monatsh Math.. 166 (2), 239-253

9

A. V. Vasilev (2005). On connection between the structure of
a finite group and the properties of its prime graph. Sib.
Math. J.. 46 (3), 396-404

10

A. V. Vasil'ev and I. B. Gorshkov (2009). On recognition of
finite groups with connected prime graph. Sib. Math. J.. 50 (2), 233-238

11

A. V. Vasil'ev and E. P. Vdovin (2005). An adjacency
criterion for the prime graph of a finite simple group. Algebra
Logic. 44 (6), 381-406

12

A. V. Vasil'ev and E. P. Vdovin (2011). Cocliques of maximal size in the prime graph of a finite simple group. Algebra Logic, Arxiv: 0905.1164v1. 50 (4), 291-322

13

K. Zsigmondy (1892). Zur theorie der potenzreste. Monatsh. Math. Phys.. 3, 265-284