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Sibirsk. Mat. Zh., 2013, Volume 54, Number 3, Pages 620–636 (Mi smj2447)  

This article is cited in 3 scientific papers (total in 3 papers)

Groups with the same prime graph as the orthogonal group $B_n(3)$

Z. Momen, B. Khosravi

Dept. of Pure Math., Faculty of Math. and Computer Sci., Amirkabir University of Technology (Tehran Polytechnic), 424, Hafez Ave., Tehran 15914, Iran

Abstract: Let $G$ be a finite group. The prime graph of $G$ is denoted by $\Gamma(G)$. It is proved in [1] that if $G$ is a finite group such that $\Gamma(G)=\Gamma(B_p(3))$, where $p>3$ is an odd prime, then $G\ge B_p(3)$ or $C_p(3)$. In this paper we prove the main result that if $G$ is a finite group such that $\Gamma(G)=\Gamma(B_n(3))$, where $n\ge6$, then $G$ has a unique nonabelian composition factor isomorphic to $B_n(3)$ or $C_n(3)$. Also if $\Gamma(G)=\Gamma(B_4(3))$, then $G$ has a unique nonabelian composition factor isomorphic to $B_4(3)$, $C_4(3)$, or $^2D_4(3)$. It is proved in [2] that if $p$ is an odd prime, then $B_p(3)$ is recognizable by element orders. We give a corollary of our result, generalize the result of [2], and prove that $B_{2k+1}(3)$ is recognizable by the set of element orders. Also the quasirecognition of $B_{2k}(3)$ by the set of element orders is obtained.

Keywords: prime graph, simple group, recognition, quasirecognition.

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English version:
Siberian Mathematical Journal, 2013, 54:3, 487–500

Bibliographic databases:

UDC: 512.54
Received: 25.08.2011

Citation: Z. Momen, B. Khosravi, “Groups with the same prime graph as the orthogonal group $B_n(3)$”, Sibirsk. Mat. Zh., 54:3 (2013), 620–636; Siberian Math. J., 54:3 (2013), 487–500

Citation in format AMSBIB
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\by Z.~Momen, B.~Khosravi
\paper Groups with the same prime graph as the orthogonal group $B_n(3)$
\jour Sibirsk. Mat. Zh.
\yr 2013
\vol 54
\issue 3
\pages 620--636
\mathnet{http://mi.mathnet.ru/smj2447}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3112620}
\transl
\jour Siberian Math. J.
\yr 2013
\vol 54
\issue 3
\pages 487--500
\crossref{https://doi.org/10.1134/S0037446613030142}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84881078485}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
    2. 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  zmath  isi  elib
    3. Mahmoudifar A., Khosravi B., “on Quasirecognition By Prime Graph of the Simple Groups a(N)(+) (P) and a(N)(-) (P)”, J. Algebra. Appl., 14:1 (2015), 1550006  crossref  mathscinet  zmath  isi  elib  scopus
  • Сибирский математический журнал Siberian Mathematical Journal
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