Timeline for Does the sequence (Number of groups of even order $\le n$) / (Number of groups of order $\leq n$) converge? If not, what are its cluster points?
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| Nov 25, 2020 at 23:53 | vote | accept | The Thin Whistler | ||
| Nov 22, 2020 at 8:25 | comment | added | Derek Holt | In this context it is worth mentioning Pyber's upper bound ${\rm gnu}(n) \le n^{(2/27)\mu(n)^2 + O(\mu(n)^{3/2})}$ on the number of groups of order $n$, where $\mu(n) \le \log_n(2)$ is the highest power of any prime dividing $n$. So the gap between proven upper and lower bounds is, in some sense, not large, it unfortunately it occurs in the exponent, rather than in the number itself. | |
| Nov 22, 2020 at 8:21 | comment | added | Alireza Abdollahi | Is this an answer or some ideas based on the above comments? | |
| Nov 22, 2020 at 0:44 | history | edited | Qiaochu Yuan | CC BY-SA 4.0 |
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| Nov 21, 2020 at 23:14 | history | edited | Qiaochu Yuan | CC BY-SA 4.0 |
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| Nov 21, 2020 at 22:33 | history | edited | Qiaochu Yuan | CC BY-SA 4.0 |
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| Nov 21, 2020 at 22:28 | history | answered | Qiaochu Yuan | CC BY-SA 4.0 |