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Sibirsk. Mat. Zh., 2013, Volume 54, Number 1, Pages 65–76 (Mi smj2401)  

This article is cited in 12 scientific papers (total in 12 papers)

On nonabelian simple groups having the same prime graph as an alternating group

M. A. Zvezdina

Novosibirsk State University, Novosibirsk, Russia

Abstract: All instances of coincidence between the prime graphs of nonabelian simple groups $G$ and $S$ are found, where $G$ is an alternating group of degree $n\ge5$ and $S$ is a nonabelian finite simple group. The precise bound of the maximal number of pairwise nonisomorphic nonabelian simple groups with the same prime graph is given in the case that one of these groups is an alternating group.

Keywords: finite simple group, alternating group, prime graph.

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English version:
Siberian Mathematical Journal, 2013, 54:1, 47–55

Bibliographic databases:

UDC: 512.542
Received: 31.10.2012

Citation: M. A. Zvezdina, “On nonabelian simple groups having the same prime graph as an alternating group”, Sibirsk. Mat. Zh., 54:1 (2013), 65–76; Siberian Math. J., 54:1 (2013), 47–55

Citation in format AMSBIB
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\paper On nonabelian simple groups having the same prime graph as an alternating group
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\pages 65--76
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. V. Maslova, “On the coincidence of Grünberg–Kegel graphs of a finite simple group and its proper subgroup”, Proc. Steklov Inst. Math. (Suppl.), 288, suppl. 1 (2015), 129–141  mathnet  crossref  mathscinet  isi  elib
    2. M. R. Zinoveva, “Konechnye prostye gruppy lieva tipa nad polem odnoi kharakteristiki s odinakovym grafom prostykh chisel”, Tr. IMM UrO RAN, 20, no. 2, 2014, 168–183  mathnet  mathscinet  elib
    3. V. A. Kovaleva, Xiaolan Yi, “Finite groups with all $n$-maximal ($n = 2, 3$) subgroups $K$-$\mathfrak{U}$-subnormal”, PFMT, 2014, no. 2(19), 59–63  mathnet
    4. A. Mahmoudifar, B. Khosravi, “On characterization by order and prime graph for alternating groups”, Siberian Math. J., 56:1 (2015), 125–131  mathnet  crossref  mathscinet  isi  elib  elib
    5. Burness T.C. Covato E., “on the Prime Graph of Simple Groups”, Bull. Aust. Math. Soc., 91:2 (2015), 227–240  crossref  mathscinet  zmath  isi  elib  scopus
    6. A. N. Skiba, “On $\sigma$-properties of finite groups III”, PFMT, 2016, no. 1(26), 52–62  mathnet
    7. M. R. Zinov'eva, “On finite simple classical groups over fields of different characteristics with coinciding prime graphs”, Proc. Steklov Inst. Math. (Suppl.), 297, suppl. 1 (2017), 223–239  mathnet  crossref  crossref  mathscinet  isi  elib
    8. B. Khosravi, A. Babai, “Simple groups with the same prime graph as $D_n(q)$”, Bull. Iran Math. Soc., 42:6 (2016), 1403–1427  mathscinet  zmath  isi
    9. A. R. Moghaddamfar, “On alternating and symmetric groups which are quasi OD-characterizable”, J. Algebra. Appl., 16:4 (2017), 1750065  crossref  mathscinet  zmath  isi  scopus
    10. A. M. Staroletov, “On recognition of alternating groups by prime graph”, Sib. elektron. matem. izv., 14 (2017), 994–1010  mathnet  crossref
    11. M. R. Zinoveva, “O konechnykh prostykh lineinykh i unitarnykh gruppakh nad polyami raznykh kharakteristik, grafy prostykh chisel kotorykh sovpadayut. I”, Tr. IMM UrO RAN, 23, no. 4, 2017, 136–151  mathnet  crossref  elib
    12. M. R. Zinoveva, “O konechnykh prostykh lineinykh i unitarnykh gruppakh malykh razmernostei nad polyami raznykh kharakteristik, grafy prostykh chisel kotorykh sovpadayut”, Tr. IMM UrO RAN, 24, no. 3, 2018, 73–90  mathnet  crossref  elib
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