Timeline for alternative construction of the quotient group
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 8, 2010 at 5:43 | comment | added | Emerton | Dear Bjorn, Yes! | |
| Feb 8, 2010 at 5:25 | comment | added | Bjorn Poonen | Restatement: Let G' be the image of G acting by left translation on the set of left cosets of N in G. (Excuse my use of the C-word!) Amusingly, when N is a non-normal subgroup, this produces the quotient by the largest normal subgroup contained in N, whereas (as remarked by Tom Church) the unknown/Brandenberg/Poonen construction produces the quotient by the smallest normal subgroup containing N. | |
| Feb 8, 2010 at 0:59 | comment | added | Martin Brandenburg | this is exactly what I've been looking for! I don't see how the universal property can be verified directly from the construction (perhaps anybody else?), but for me it's sufficient that $p : G \to G'$ is a surjektive homomorphism with kernel exactly $N$. | |
| Feb 8, 2010 at 0:58 | vote | accept | Martin Brandenburg | ||
| Feb 7, 2010 at 21:04 | history | answered | Emerton | CC BY-SA 2.5 |