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14.66 (1999)

Solved

(Well-known problem). Let $G$ be a finite soluble group, $\pi(G)$ the set of primes dividing the order of $G$, and $\nu(G)$ the maximum number of primes dividing the order of some element. Does there exist a linear bound for $|\pi(G)|$ in terms of $\nu(G)$?

Contributor: A. Moretó

Progress

Yes, it does (T. M. Keller, J. Algebra, 178, no. 2 (1995), 643–652).

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