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13.65 (1995)

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A finite simple group is called a $K_n$-group if its order is divisible by exactly $n$ different primes. The number of $K_3$-groups is known to be 8. The $K_4$-groups are classified mod CFSG (W. J. Shi, in: Group Theory in China (Math. Appl., 365), Kluwer, 1996, 163–181) and some significant further results are obtained in (Yann Bugeaud, Zhenfu Cao, M. Mignotte, J. Algebra, 241 (2001), 658–668). But the question remains: is the number of $K_4$-groups finite or infinite?

Contributor: W. J. Shi

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