Timeline for Maximal commuting subsets of $\text{End}(X)$
Current License: CC BY-SA 3.0
16 events
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| Feb 22, 2017 at 8:12 | vote | accept | Dominic van der Zypen | ||
| Feb 5, 2017 at 17:56 | answer | added | Ehud Meir | timeline score: 1 | |
| Feb 5, 2017 at 14:12 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jan 6, 2017 at 13:41 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Dec 7, 2016 at 12:59 | history | edited | YCor |
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| Dec 7, 2016 at 11:11 | history | edited | Dominic van der Zypen | CC BY-SA 3.0 |
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| Dec 7, 2016 at 3:59 | comment | added | YCor | $\mathrm{End}(X)=X^X$ is a separable topological semigroup, and for $X$ countable is a Polish space. Every maximal abelian subsemigroup is thus a closed subset. A closed subset in a Polish space cannot have cardinal between $\aleph_0$ and $2^{\aleph_0}$ (regardless of Continuum Hypothesis). | |
| Dec 6, 2016 at 19:09 | comment | added | Todd Leason | @Dominic: Do you know what the maximal commuting subsets are for X finite ? | |
| Dec 6, 2016 at 17:03 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Nov 6, 2016 at 17:02 | comment | added | Anthony Quas | I believe there is an Abelian group of every cardinality, so it should be possible to have an $M$ of size $|X|$: impose a group structure on $X$ and define a map for each $x\in X$ by $f_x(y)=x+y$. These clearly commute. It should be easy to show these don't commute with anything else, so are maximal. | |
| Nov 6, 2016 at 16:06 | comment | added | Goldstern | If you are interested in groups rather than semigroups, have a look at Shelah+Steprans, Fund.Math. 2007, MR2353856. | |
| Nov 6, 2016 at 15:19 | answer | added | Gerhard Paseman | timeline score: 1 | |
| Nov 6, 2016 at 15:17 | history | edited | Dominic van der Zypen | CC BY-SA 3.0 |
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| Nov 6, 2016 at 15:12 | comment | added | Dominic van der Zypen | Thanks both of you for your comments. As I see it, what I call "maximal commuting" sets will always contain the identity (because you can always add the identity to any commuting set, and it stays commuting) | |
| Nov 6, 2016 at 14:34 | comment | added | მამუკა ჯიბლაძე | @HeinrichD Well, submonoids actually | |
| Nov 6, 2016 at 13:59 | history | asked | Dominic van der Zypen | CC BY-SA 3.0 |