Quasirecognition by prime graph of finite simple Groups 2Dn(3)

Khosravi, Behrooz; Moradi, Hossein

doi:10.22108/ijgt.2014.5254

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	Quasirecognition by prime graph of finite simple Groups ²D_n(3)
International Journal of Group Theory
مقاله 7، دوره 3، شماره 4، اسفند 2014، صفحه 47-56 اصل مقاله (309.07 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/ijgt.2014.5254
نویسندگان
Behrooz Khosravi^* ؛ Hossein Moradi
Amirkabir University of Technology
چکیده
‎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 ‎$D$‎.
کلیدواژه‌ها
prime graph؛ simple group؛ linear group؛ quasirecognition

مراجع
A. Babai and B. Khosravi (2011) Recognition by prime graph of $^2D_{2^m+1}(3)$ Sib. Math. J. 52 (5), 788-795 A. Babai, B. Khosravi and N. Hasani (2009) Quasirecognition by prime graph of $^2D_p(3)$ where $p=2^n+1\geq 5$ is a prime Bull. Malays. Math. Sci. Soc. (2) 32 (3), 343-350 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 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 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 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 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 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 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 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 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 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 K. Zsigmondy (1892) Zur theorie der potenzreste Monatsh. Math. Phys. 3, 265-284
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Quasirecognition by prime graph of finite simple Groups ²D_n(3)