Timeline for Ratio of number of subgroups to the order of a finite group
Current License: CC BY-SA 3.0
11 events
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| Aug 24, 2012 at 18:07 | comment | added | Will Sawin | It's not clear if "related" is even well-defined enough here to give that question a satisfying answer. Which mathematical statements are related to $2+2=2\times 2$? | |
| Aug 24, 2012 at 6:47 | history | edited | Qiaochu Yuan | CC BY-SA 3.0 |
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| Aug 24, 2012 at 6:20 | history | edited | Qiaochu Yuan | CC BY-SA 3.0 |
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| Aug 24, 2012 at 4:49 | comment | added | Qiaochu Yuan | @Will: I had other other reasons in mind (for example the fact that $\Lambda^2(\mathbb{R}^4)$ is not an irreducible representation of $\text{SO}(4)$) but who knows, maybe they're all related. | |
| Aug 24, 2012 at 4:28 | comment | added | Will Sawin | Isn't that just dependent on whether $n=\max_{k=0}^n k(n-k)$ - the max of the dimension of the various Grassmanians, since the number of points on an algebraic variety of dimension $d$ goes to $p^d$ as $p\to \infty$ by the Weil conjectures? It doesn't seem plausible to me that there are exotic $\mathbb R^4$s because $\operatorname{Gr}_2^2$ is $4$-dimensional, but I know nothing of the relevant topology and certainly stranger things have happened. | |
| Aug 24, 2012 at 3:44 | history | edited | Qiaochu Yuan | CC BY-SA 3.0 |
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| Aug 24, 2012 at 3:30 | comment | added | Qiaochu Yuan | Curiously $4$ is the only dimension $d$ in which $R(C_p^d)$ approaches $1$ as $p \to \infty$, and the reason is something happening in the middle dimension. I wonder if this is related to the other reasons that $4$ is an exceptional dimension... | |
| Aug 24, 2012 at 2:04 | history | undeleted | Qiaochu Yuan | ||
| Aug 24, 2012 at 2:03 | history | edited | Qiaochu Yuan | CC BY-SA 3.0 |
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| Aug 24, 2012 at 1:44 | history | deleted | Qiaochu Yuan | ||
| Aug 24, 2012 at 0:36 | history | answered | Qiaochu Yuan | CC BY-SA 3.0 |