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Sibirsk. Mat. Zh., 2008, Volume 49, Number 4, Pages 934–944 (Mi smj1890)  

This article is cited in 24 scientific papers (total in 24 papers)

2-Recognizability by prime graph of $PSL(2,p^2)$

A. Khosravia, B. Khosravibc

a Faculty of Mathematical Sciences and Computer Engineering, University For Teacher Education
b Institute for Studies in Theoretical Physics and Mathematics
c 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 and let $\Gamma(G)$ be the prime graph of $G$. Assume $p$ prime. We determine the finite groups $G$ such that $\Gamma(G)=\Gamma(PSL(2,p^2))$ and prove that if $p\ne2,3,7$ is a prime then $k(\Gamma(PSL(2,p^2)))=2$. We infer that if $G$ is a finite group satisfying $|G|=|PSL(2,p^2)|$ and $\Gamma(G)=\Gamma(PSL(2,p^2))$ then $G\cong PSL(2,p^2)$. This enables us to give new proofs for some theorems; e.g., a conjecture of W. Shi and J. Bi. Some applications are also considered of this result to the problem of recognition of finite groups by element orders.

Keywords: simple group, prime graph, element order, linear group.

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English version:
Siberian Mathematical Journal, 2008, 49:4, 749–757

Bibliographic databases:

UDC: 519.542
Received: 05.06.2006
Revised: 16.10.2007

Citation: A. Khosravi, B. Khosravi, “2-Recognizability by prime graph of $PSL(2,p^2)$”, Sibirsk. Mat. Zh., 49:4 (2008), 934–944; Siberian Math. J., 49:4 (2008), 749–757

Citation in format AMSBIB
\by A.~Khosravi, B.~Khosravi
\paper 2-Recognizability by prime graph of $PSL(2,p^2)$
\jour Sibirsk. Mat. Zh.
\yr 2008
\vol 49
\issue 4
\pages 934--944
\jour Siberian Math. J.
\yr 2008
\vol 49
\issue 4
\pages 749--757

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    This publication is cited in the following articles:
    1. Khosravi B., “$n$-recognition by prime graph of the simple group $\mathrm{PSL}(2,q)$”, J. Algebra Appl., 7:6 (2008), 735–748  crossref  mathscinet  zmath  isi  elib  scopus
    2. Babai A., Khosravi B., Hasani N., “Quasirecognition by prime graph of $ ^2D_p(3)$ where $p=2^n+1\ge 5$ is a prime”, Bull. Malays. Math. Sci. Soc. (2), 32:3 (2009), 343–350  mathscinet  zmath  isi
    3. A. S. Kondratev, I. V. Khramtsov, “O konechnykh triprimarnykh gruppakh”, Tr. IMM UrO RAN, 16, no. 3, 2010, 150–158  mathnet  elib
    4. Akhlaghi Z., Khosravi B., Khatami M., “Characterization by prime graph of $\mathrm{PGL}(2,p^k)$ where $p$ and $k>1$ are odd”, Internat. J. Algebra Comput., 20:7 (2010), 847–873  crossref  mathscinet  zmath  isi  elib  scopus
    5. 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  scopus
    6. Khatami M., Khosravi B., Akhlaghi Z., “A new characterization for some linear groups”, Monatsh. Math., 163:1 (2011), 39–50  crossref  mathscinet  zmath  isi  scopus
    7. 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  scopus
    8. Khosravi B., Babai A., “Quasirecognition by prime graph of $F_4(q)$ where $q=2^n>2$”, Monatsh. Math., 162:3 (2011), 289–296  crossref  mathscinet  zmath  isi  elib  scopus
    9. A. Babai, B. Khosravi, “Recognition by prime graph of $^2D_{2m+1}(3)$”, Siberian Math. J., 52:5 (2011), 788–795  mathnet  crossref  mathscinet  isi
    10. A. S. Kondrat'ev, I. V. Khramtsov, “On finite tetraprimary groups”, Proc. Steklov Inst. Math. (Suppl.), 279, suppl. 1 (2012), 43–61  mathnet  crossref  isi  elib
    11. Khatami M., Khosravi B., Akhlaghi Z., “NCF-distinguishablity by prime graph of $PGL(2,p)$ where $p$ is a prime”, Rocky Mountain J. Math., 41:5 (2011), 1523–1545  crossref  mathscinet  zmath  isi  elib  scopus
    12. 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
    13. 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  scopus
    14. 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  scopus
    15. 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
    16. M. A. Zvezdina, “On nonabelian simple groups having the same prime graph as an alternating group”, Siberian Math. J., 54:1 (2013), 47–55  mathnet  crossref  mathscinet  isi
    17. 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
    18. 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
    19. Akhilaghi Z. Khatami M. Khosravi B., “On the Prime Graph of D-N(Q) Where Q Is an Element of (2,5)”, Quaest. Math., 36:4 (2013), 517–535  crossref  mathscinet  isi  scopus
    20. 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  mathscinet  zmath  isi  elib  elib
    21. 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  scopus
    22. 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  scopus
    23. 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
    24. Moradi H., Darafsheh M.R., Iranmanesh A., “Quasirecognition By Prime Graph of the Groups D-2(2N)(Q) Where Q < 10(5)”, Mathematics, 6:4 (2018), 57  crossref  isi  scopus
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