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

This article is cited in 9 scientific papers (total in 9 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.

Full text (in Russian): PDF file (294 kB)
References (in Russian): PDF file   HTML файл

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

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
    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
    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
    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
    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  zmath
    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
    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  elib
    8. З. Момен, Б. Хосрави, “Группы с тем же графом простых чисел, что и ортогональная группа $B_n(3)$”, Сиб. матем. журн., 54:3 (2013), 620–636  mathnet  mathscinet; 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  crossref
    9. А. Бабаи, Б. Хосрави, “Квазираспознаваемость $^2D_{n}(3^\alpha)$ по графу простых чисел при $n=4m+1\ge 21$ и нечетном $\alpha$”, Матем. заметки, 95:3 (2014), 323–334  mathnet  crossref; 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  crossref
  • Сибирский математический журнал Siberian Mathematical Journal
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