Timeline for Characterization of the elements of an infinite simple group
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Nov 22, 2012 at 16:55 | comment | added | Stefan Kohl♦ | By the way -- I asked this question already in 2010 as Problem 17.59 in the Kourovka Notebook. | |
| Nov 15, 2012 at 21:18 | comment | added | Stefan Kohl♦ | I don't see how this should help -- but maybe you have some good idea? One also has a continuous action of ${\rm CT}(\mathbb{Z})$ on $\mathbb{Z}$, endowed with a topology by taking the set of all residue classes as a basis -- but I don't see so far that this helps further. But maybe you have better luck with your approach. By the way, I prefer the notation ${\rm RCWA}(\mathbb{Z})$ for the group of all residue-class-wise affine permutations (that's the notation I used in my publications so far). | |
| Nov 15, 2012 at 19:20 | comment | added | YCor | I would certainly call $CT(\mathbf{Z})$ the group of all residue-class-wise affine permutations of $\mathbf{Z}$, while the group you consider (or the possibly larger stabilizer of $\mathbf{N}$) looks like an interesting subgroup, but as a kind of stabilizer. Anyway, let $CT'(\mathbf{Z})$ be the big group: then the action of this large group extends to a continuous action on the profinite completion $\hat{\mathbf{Z}}$. This should help understanding it. | |
| Nov 15, 2012 at 14:08 | history | edited | Stefan Kohl♦ | CC BY-SA 3.0 |
Fixed a typo.
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| Nov 15, 2012 at 10:24 | history | asked | Stefan Kohl♦ | CC BY-SA 3.0 |