Timeline for Do all possible trees arise as orbit trees of some permutation groups?
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
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| Jun 25, 2013 at 3:02 | history | bounty ended | CommunityBot | ||
| Apr 24, 2011 at 23:58 | history | edited | Mingzhi Xuan | CC BY-SA 3.0 |
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| Apr 24, 2011 at 23:57 | comment | added | Mingzhi Xuan | a rooted tree is a subset(well, my fault) in \omega^{<\omega} that is closed under taking initial segment. For example, the set {(0),(0,0),(0,1),(0,2)} is the tree that has one root and three "branches", each terminates at level 1. But we usually think of it intuitively(as drawn on paper). As we fix more and more points in N, the orbits become smaller and smaller as a set. We intuitively draw a node for each orbit with infinite size. If O2 is a subset of O1, then N2(on the level below) is linked to N1. Thus we may draw the orbit tree. | |
| Apr 24, 2011 at 23:42 | comment | added | Mingzhi Xuan | Thank you for your comment. G_1 could have infinitely many orbits. But your construction will not obtain the wanted direct product. This is because g(a1,a2...)g^{-1}=(g(a1),g(a2)...) and it will introduce a lot more permutations. | |
| Apr 24, 2011 at 7:10 | comment | added | Nishant Chandgotia | How are you relating a tree to an element in \omega^{<\omega}? Does this mean all finite sequences in natural numbers? If so why does the tree need to be finite? Probably I am misunderstanding the notation. Can you clarify? | |
| Apr 24, 2011 at 6:54 | comment | added | Nishant Chandgotia | Can't G1 have infinitely many orbits? Construct your group in the following fashion. Divide N into {1} and countably more disjoint infinite sets Sis. Let G be generated by transpositions between the 1 and the first element of Sis and the full permutation group on Si. I was not sure how G corresponded to the rooted tree | |
| Apr 18, 2011 at 7:32 | history | edited | Did | CC BY-SA 3.0 |
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| Apr 18, 2011 at 6:04 | history | bounty started | Mingzhi Xuan | ||
| Apr 12, 2011 at 17:20 | history | edited | Mingzhi Xuan | CC BY-SA 3.0 |
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| Apr 12, 2011 at 15:48 | history | edited | Mingzhi Xuan | CC BY-SA 3.0 |
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| Apr 12, 2011 at 13:39 | history | edited | Mingzhi Xuan | CC BY-SA 3.0 |
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| Apr 12, 2011 at 13:33 | history | edited | Mingzhi Xuan | CC BY-SA 3.0 |
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| Apr 12, 2011 at 4:55 | history | edited | Mingzhi Xuan |
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| Apr 12, 2011 at 4:16 | history | edited | Mingzhi Xuan | CC BY-SA 3.0 |
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| Apr 12, 2011 at 4:09 | history | edited | Mingzhi Xuan | CC BY-SA 3.0 |
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| Apr 12, 2011 at 4:02 | history | asked | Mingzhi Xuan | CC BY-SA 3.0 |