Timeline for Could groups be used instead of sets as a foundation of mathematics?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| May 8, 2022 at 11:49 | history | edited | David Roberts♦ | CC BY-SA 4.0 |
replaced broken project Euclid link with doi and jstor link; corrected title
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| Feb 12, 2020 at 23:03 | history | edited | user44143 | CC BY-SA 4.0 |
small cleans
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| Feb 12, 2020 at 15:37 | history | edited | user44143 | CC BY-SA 4.0 |
fixed definition of Z, following Simon Henry's suggestion
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| Feb 12, 2020 at 15:33 | comment | added | Simon Henry | That sounds right: "Almost free groups" have to be non zero and torsion free so there is always a mono from $\mathbb{Z}$, and only $\mathbb{Z}$ (and $0$) has mono to $\mathbb{Z}$. | |
| Feb 12, 2020 at 15:30 | comment | added | user44143 | @SimonHenry, suppose we define that a group $H$ is almost free iff it is not 1, and for every $G$ other than $1$, there is a non-constant map from $H$ to $G$. Then is $\mathbb{Z}$ the unique almost free group with monos into all other almost free groups? | |
| Feb 12, 2020 at 15:18 | comment | added | Simon Henry | The third bullet point in claim 3 (the characterization of $\mathbb{Z}$) does not work: all free groups have this property, More generally any group of the form $H * \mathbb{Z}$ have the property as well. | |
| Feb 12, 2020 at 14:40 | comment | added | user44143 | @ArnaudD., I fixed the definition of quotients. | |
| Feb 12, 2020 at 14:39 | history | edited | user44143 | CC BY-SA 4.0 |
corrected definition of quotient
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| Feb 12, 2020 at 13:04 | comment | added | Arnaud D. | Also, your characterization of quotients and normal subgroups seems fishy to me : with the way you phrased it, it seems to me that $G/H=\{1\}$ for all subgroups of $G$. | |
| Feb 12, 2020 at 12:59 | comment | added | Arnaud D. | I'm not sure it counts as a characterization in the language of ETCG, but you can also characterize abelian groups as the internal monoids (or even just the internal unitary magmas) in the category of groups, thanks to the Eckmann-Hilton argument. | |
| Feb 12, 2020 at 4:04 | history | edited | user44143 | CC BY-SA 4.0 |
edited body
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| Feb 12, 2020 at 3:36 | history | answered | user44143 | CC BY-SA 4.0 |