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Sibirsk. Mat. Zh., 2009, Volume 50, Number 2, Pages 446–452 (Mi smj1971)  

This article is cited in 15 scientific papers (total in 15 papers)

Quasirecognition by prime graph of $L_{10}(2)$

B. Khosravi

Dept. of Pure Math., Faculty of Math. and Computer Sci., Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran

Abstract: Let $G$ be a finite group. The prime graph of $G$ is denoted by $\Gamma(G)$. The main result we prove is as follows: If $G$ is a inite group such that $\Gamma(G)=\Gamma(L_{10}(2))$ then $G/O_2(G)$ is isomorphic to $L_{10}(2)$. In fact we obtain the first example of a finite group with the connected prime graph which is quasirecognizable by its prime graph. As a consequence of this result we can give a new proof for the fact that the simple group $L_{10}(2)$ is uniquely determined by the set of its element orders.

Keywords: prime graph, finite group, projective special linear group.

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English version:
Siberian Mathematical Journal, 2009, 50:2, 355–359

Bibliographic databases:

UDC: 512.542
Received: 03.10.2007

Citation: B. Khosravi, “Quasirecognition by prime graph of $L_{10}(2)$”, Sibirsk. Mat. Zh., 50:2 (2009), 446–452; Siberian Math. J., 50:2 (2009), 355–359

Citation in format AMSBIB
\by B.~Khosravi
\paper Quasirecognition by prime graph of~$L_{10}(2)$
\jour Sibirsk. Mat. Zh.
\yr 2009
\vol 50
\issue 2
\pages 446--452
\jour Siberian Math. J.
\yr 2009
\vol 50
\issue 2
\pages 355--359

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    This publication is cited in the following articles:
    1. Khosravi B., Moradi H., “Quasirecognition by prime graph of finite simple groups $L_n(2)$ and $U_n(2)$”, Acta Math. Hungar., 132:1-2 (2011), 140–153  crossref  mathscinet  zmath  isi  elib
    2. Khosravi B., Akhlaghi Z., Khatami M., “Quasirecognition by prime graph of simple group $D_n(3)$”, Publ. Math. Debrecen, 78:2 (2011), 469–484  crossref  mathscinet  zmath  isi
    3. Ghasemabadi M.F., Iranmanesh A., “Quasirecognition by the prime graph of the group $C_n(2)$, where $n \ne 3$ is odd”, Bull. Malays. Math. Sci. Soc. (2), 34:3 (2011), 529–540  mathscinet  zmath  isi
    4. Ghasemabadi M.F. Iranmanesh A., “2-Quasirecognizability of the Simple Groups B-N(P) and C-N(P) by Prime Graph”, Bull. Iran Math. Soc., 38:3 (2012), 647–668  mathscinet  zmath  isi
    5. Nosratpour P., Darafsheh M.R., “Recognition of the Groups l (5)(4) and U (4)(4) by the Prime Graph”, Ukr. Math. J., 64:2 (2012), 238–246  crossref  mathscinet  zmath  isi  elib
    6. Babai A. Khosravi B., “On the Composition Factors of a Group with the Same Prime Graph as B (N) (5)”, Czech. Math. J., 62:2 (2012), 469–486  crossref  mathscinet  zmath  isi  elib
    7. Khosravi B. Moradi H., “Quasirecognition by Prime Graph of Some Orthogonal Groups Over the Binary Field”, J. Algebra. Appl., 11:3 (2012), 1250056  crossref  mathscinet  zmath  isi  elib
    8. Z. Momen, B. Khosravi, “Groups with the same prime graph as the orthogonal group $B_n(3)$”, Siberian Math. J., 54:3 (2013), 487–500  mathnet  crossref  mathscinet  isi
    9. Amiri S.S.S. Asboei A.R.Kh. Iranmanesh A. Tehranian A., “Quasirecognition by the Prime Graph of l-3(G) Where 3 < Q < 100”, Bull. Iran Math. Soc., 39:2 (2013), 289–305  mathscinet  zmath  isi
    10. A. Babai, B. Khosravi, “Quasirecognition by Prime Graph of $^2D_{n}(3^\alpha)$ where $n=4m+1\ge 21$ and $\alpha$ is Odd”, Math. Notes, 95:3 (2014), 293–303  mathnet  crossref  crossref  isi  elib  elib
    11. Babai A. Khosravi B., “Groups With the Same Prime Graph as the Simple Group D (N) (5)”, Ukr. Math. J., 66:5 (2014), 666–677  crossref  mathscinet  zmath  isi  elib
    12. Khosravi B. Khosravi B. Oskouei Hamid Reza Dalili, “on Recognition By Prime Graph of the Projective Special Linear Group Over Gf(3)”, Publ. Inst. Math.-Beograd, 95:109 (2014), 255–266  crossref  mathscinet  zmath  isi
    13. Momen Z. Khosravi B., “Quasirecognition By Prime Graph of the Simple Group Bn (9)”, Proc. Rom. Acad. Ser. A-Math. Phys., 16:3 (2015), 397–404  mathscinet  isi  elib
    14. Babai A. Khosravi B., “Quasirecognition By Prime Graph of l-N(2(Alpha)) For Some N and Alpha”, Math. Rep., 17:1 (2015), 119–132  mathscinet  zmath  isi  elib
    15. Nosratpour P., Darafsheh M.R., “Characterization of the Group G(2)(5) By the Prime Graph”, Ukr. Math. J., 68:8 (2017), 1308–1313  crossref  isi
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