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15.99 (2002)

Open

Let $f(n)$ be the number of isomorphism classes of finite groups of order $n$. Is it true that the equation $f(n) = k$ has a solution for any positive integer $k$?

Contributor: W. J. Shi

Progress

The answer is affirmative for all $k \leqslant 1000$ (G. M. Wei, Southeast Asian Bull. Math., 22, no. 1 (1998), 93–102).

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