Timeline for When does a transitive action of a profinite group have an infinite orbit?
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Oct 18, 2009 at 0:25 | comment | added | S. Carnahan♦ | If the action is regular, then your criterion is equivalent to the open problem. | |
| Oct 16, 2009 at 20:32 | comment | added | John Goodrick | Indeed, it does smell a lot like it. If anybody has a proof that the two statements are actually equivalent, I'd love to see it. | |
| Oct 14, 2009 at 2:54 | comment | added | S. Carnahan♦ | Your proposed criterion smells a lot like the open problem you mentioned in that other thread: whether profinite groups with elements of arbitrarily large order can be torsion. | |
| Oct 14, 2009 at 0:01 | comment | added | John Goodrick | Yes, the case I'm interested in is when X is a projective limit of finite discrete spaces and G acts continuously on X. Another way to think about it is you have a 1-transitive infinite permutation group (G,X) which is a projective limit of finite permutation groups (G_i, X_i). | |
| Oct 13, 2009 at 15:33 | comment | added | Ben Webster♦ | I think you definitely want to consider sets with inverse limit topologies. I mean, where's the fun in finite actions of profinite groups (I mean, aside from all of Galois theory). | |
| Oct 13, 2009 at 15:21 | history | answered | S. Carnahan♦ | CC BY-SA 2.5 |