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This might be a stupid question, but here it goes:

Is anything known about, whether:

$$\lim_{n\to \infty} \frac{\#\{\text{Groups of order }2^n\}}{\#\{\text{Groups of order} \leq 2^n\}} = 1$$

(where two groups are considered the same, if they are isomorphic).

Stefan Perko
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  • Possible related (not the same): http://math.stackexchange.com/questions/456419, http://math.stackexchange.com/questions/241369 – Watson Jun 23 '16 at 12:00
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    @Watson It is more than "possibly related". It says that the above question is still an open conjecture, and gives known asymptotics in this direction. – Dietrich Burde Jun 23 '16 at 12:03
  • @DietrichBurde I wasn't sure, what exactly was meant by "almost all finite groups are $2$-groups". – Stefan Perko Jun 23 '16 at 12:05

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