Timeline for Do all exact sequences $0 \rightarrow A \rightarrow A \oplus B \rightarrow B \rightarrow 0$ split for finitely generated abelian groups?
Current License: CC BY-SA 3.0
12 events
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| Jul 16, 2019 at 20:06 | history | edited | Martin Sleziak |
Removed the deprecated (abstract-algebra) tag - see the tag info: https://mathoverflow.net/tags/abstract-algebra/info (if there are some other suitable tags, choose them instead.)
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| Jul 16, 2019 at 15:17 | answer | added | Sean Lawton | timeline score: 7 | |
| May 20, 2014 at 17:01 | comment | added | Arturo Magidin | @Fernando: Oops... I wonder what I was thinking. | |
| May 20, 2014 at 16:47 | vote | accept | Felix Y. | ||
| May 20, 2014 at 16:43 | answer | added | Steven Landsburg | timeline score: 30 | |
| May 20, 2014 at 16:37 | comment | added | Fernando Muro | @ArturoMagidin your $C$ doesn't split as $A\oplus B$. | |
| May 20, 2014 at 16:37 | comment | added | YCor | Obviously in the the question homomorphisms are arbitrary, not the canonical ones. The answer is "yes, they're all split" by Landsburg's answer, see the link given by Dag Oskar Madsen. | |
| May 20, 2014 at 16:14 | comment | added | Dag Oskar Madsen | See Steven Landsburg's answer to the following question: mathoverflow.net/questions/157938/… | |
| May 20, 2014 at 16:07 | comment | added | YCor | @Alberto: that $0\to N\to G\to Q\to 0$ splits means that the map $Q\to G$ lifts the projection $G\to Q$. This can fail with the canonical inclusion. | |
| May 20, 2014 at 15:58 | comment | added | R.P. | It isn't stated what the maps are, so it is not clear that that would give a splitting. | |
| May 20, 2014 at 15:44 | comment | added | Alicia Garcia-Raboso | What's wrong with the canonical inclusion $B \to A \oplus B$ ? | |
| May 20, 2014 at 15:37 | history | asked | Felix Y. | CC BY-SA 3.0 |