Timeline for Quotients of Abelian Groups
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 24, 2013 at 4:15 | comment | added | user4535 | There are certainly several cases of my question that are uninteresting. In the case I actually am interested in, A+B is a proper subgroup of G and C is smaller than $A \cap B$ but still bigger than just $1$. | |
| Feb 24, 2013 at 0:36 | comment | added | Wei Zhou | The only case that need to be considered is that $C=1$. And now the equation is $D/(A+B) \cong A \cap B$. In general, this is not true. So there need some additional restrictions. | |
| Feb 23, 2013 at 15:18 | comment | added | user6976 | If $A+B=G$, then the only option for $D$ is $G$. So you want in that case $G/(A+B)=1=(A\cap B)/C$. This can only happen when $C=A\cap B$. This rarely happens if $A\cap B$ is large. Perhaps some conditions are missing. On the other hand, if $A\cap B=1$, then you can take $D=A+B$. | |
| Feb 23, 2013 at 14:52 | history | asked | user4535 | CC BY-SA 3.0 |