A prime graph of a finite group is defined in the following way: the set of vertices of the graph is the set of prime divisors of the order of the group, and two distinct vertices r and s are joined by an edge if there is an element of order rs in the group. We describe all cocliques of maximal size for finite simple groups.
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References
A. V. Vasil’ev and E. P. Vdovin, “An adjacency criterion for the prime graph of a finite simple group,” Algebra Logika, 44, No. 6, 682–725 (2005).
J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, and R. A. Wilson, Atlas of Finite Groups, Clarendon Press, Oxford (1985).
The GAP Group, GAP—Groups, Algorithms, and Programming, Vers. 4.4.12 (2008); http://www.gap-system.org.
K. Zsigmondy, “Zur Theorie der Potenzreste,” Monatsh. Math. Phys., 3, 265–284 (1892).
M. Roitman, “On Zsigmondy primes,” Proc. Am. Math. Soc., 125, No. 7, 1913–1919 (1997).
A. V. Zavarnitsine, “Recognition of the simple groups L 3(q) by element orders,” J. Group Theory, 7, No. 1, 81–97 (2004).
A. S. Kondratiev, “Subgroups of finite Chevalley groups,” Usp. Mat. Nauk, 41, No. 1(247), 57–96 (1986).
R. W. Carter, “Conjugacy classes in the Weyl group,” Comp. Math., 25, No. 1, 1–59 (1972).
A. V. Zavarnitsine, “Recognition of finite groups by the prime graph,” Algebra Logika, 45, No. 4, 390–408 (2006).
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Translated from Algebra i Logika, Vol. 50, No. 4, pp. 425–470, July-August, 2011.
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Vasil’ev, A.V., Vdovin, E.P. Cocliques of maximal size in the prime graph of a finite simple group. Algebra Logic 50, 291–322 (2011). https://doi.org/10.1007/s10469-011-9143-8
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DOI: https://doi.org/10.1007/s10469-011-9143-8