Abstract:
All instances of coincidence between the prime graphs of nonabelian simple groups GG and SS are found, where GG is an alternating group of degree n⩾5 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.
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
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\by M.~A.~Zvezdina
\paper On nonabelian simple groups having the same prime graph as an alternating group
\jour Sibirsk. Mat. Zh.
\yr 2013
\vol 54
\issue 1
\pages 65--76
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\jour Siberian Math. J.
\yr 2013
\vol 54
\issue 1
\pages 47--55
\crossref{https://doi.org/10.1134/S0037446613010072}
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Linking options:
https://www.mathnet.ru/eng/smj2401
https://www.mathnet.ru/eng/smj/v54/i1/p65
This publication is cited in the following 15 articles:
M. R. Zinov'eva, “On Finite Simple Groups of Exceptional Lie Type over Fields of Different Characteristics with Coinciding Prime Graphs”, Proc. Steklov Inst. Math. (Suppl.), 313, suppl. 1 (2021), S228–S240
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Buturlakin A.A. Vasil'ev A.V., “the Graph of Atomic Divisors and Recognition of Finite Simple Groups”, J. Algebra, 537 (2019), 478–502
M. R. Zinov'eva, “On finite simple linear and unitary groups of small size over fields of different characteristics with coinciding prime graphs”, Proc. Steklov Inst. Math. (Suppl.), 307, suppl. 1 (2019), S179–S195
A. R. Moghaddamfar, “On alternating and symmetric groups which are quasi OD-characterizable”, J. Algebra. Appl., 16:4 (2017), 1750065
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M. R. Zinov'eva, “On finite simple linear and unitary groups over fields of different characteristics with coinciding prime graphs. I”, Proc. Steklov Inst. Math. (Suppl.), 304, suppl. 1 (2019), S186–S202
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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
B. Khosravi, A. Babai, “Simple groups with the same prime graph as $D_n(q)$”, Bull. Iran Math. Soc., 42:6 (2016), 1403–1427
A. Mahmoudifar, B. Khosravi, “On characterization by order and prime graph for alternating groups”, Siberian Math. J., 56:1 (2015), 125–131
Burness T.C. Covato E., “on the Prime Graph of Simple Groups”, Bull. Aust. Math. Soc., 91:2 (2015), 227–240
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
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
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
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