We deal with finite simple groups G with the property π(G) ⊆ {2, 3, 5, 7, 11, 13, 17}, where π(G) is the set of all prime divisors of the order of a group G. The set of all such groups is denoted by ζ 17. Thompson’s conjecture in [1, Question 12.38] is proved valid for all groups in ζ 17 whose prime graph is connected.
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Supported by RFBR (grant No. 11-01-00456-a), by the Grants Council (under RF President) for State Aid of Leading Scientific Schools (grant NSh-3669.2010.1), by the Grants Council (under RF President) for State Aid of Young Doctors of Science (project MD-2587.2010.1), and by the Russian Ministry of Education through the Analytical Departmental Target Program “Development of Scientific Potential of the Higher School of Learning” (project No. 2.1.1.10726).
Translated from Algebra i Logika, Vol. 51, No. 2, pp. 168-192, March-April, 2012.
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Gorshkov, I.B. Thompson’s conjecture for simple groups with connected prime graph. Algebra Logic 51, 111–127 (2012). https://doi.org/10.1007/s10469-012-9175-8
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DOI: https://doi.org/10.1007/s10469-012-9175-8