Timeline for Action of a profinite group
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| May 1, 2014 at 9:49 | comment | added | Jeremy Rickard | That should read "does answer question 2 in the negative". I think the same example also answers question 3 in the negative. | |
| May 1, 2014 at 9:38 | comment | added | Jeremy Rickard | Ignore my previous comment: I think I was confused, and Julian's example does answers question in the negative, even over $\mathbb{Z}_p$. | |
| Apr 30, 2014 at 19:10 | comment | added | Pablo | What if $G$ is of order coprime to $p$? Can we say something in the $\mathbb{Z}_p$ case then? | |
| Apr 30, 2014 at 18:46 | comment | added | Jeremy Rickard | In Julian's example, I think that $(p^2,1,0,0,\dots)$ and $(p^2,p,0,0,\dots)$ generate closed submodules with trivial intersection, so the counterexample that works over $\mathbb{F}_p$ doesn't seem to generalize in a straightforward way to $\mathbb{Z}_p$. | |
| Apr 30, 2014 at 17:15 | comment | added | Pablo | Yes, you are right. I am still curious about the case of $\mathbb{Z}_p$. What happens there? | |
| Apr 30, 2014 at 16:12 | comment | added | Jeremy Rickard | I hadn't noticed this question before. You probably realize this, but Julian's example, done over $\mathbb{F}_p$ instead of $\mathbb{Z}_p$, is precisely the Pontryagin dual of the example I gave in the other thread. Unfortunately, over $\mathbb{Z}_p$ it doesn't give an answer to question 2. | |
| Apr 30, 2014 at 15:32 | vote | accept | Pablo | ||
| May 1, 2014 at 11:27 | |||||
| Apr 30, 2014 at 15:32 | history | answered | Pablo | CC BY-SA 3.0 |