Timeline for Classification of countable subgroups of the circle
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 17, 2011 at 14:19 | vote | accept | Joanna K-P | ||
| Nov 17, 2011 at 14:18 | vote | accept | Joanna K-P | ||
| Nov 17, 2011 at 14:18 | |||||
| Nov 16, 2011 at 14:51 | comment | added | Alain Valette | The question is equivalent to describing the countable additive subgroups of $\mathbb{R}$ containing 1: if $A$ is such a group, write $A=D\oplus C$, where $D$ is divisible and $C$ is reduced (= no non-zero divisible subgroup). $D$ is the easy part: a vector space over $\mathbb{Q}$, hence classified by dimension. $C$ is the tricky part: you should look at the rank, but my knowledge stops short (rank 1 is equivalent to being isomorphic to a subgroup of $\mathbb{Q}$). See "Infinite abelian groups" in en.wikipedia.org/wiki/Abelian_group to have an idea of the difficulty of the question. | |
| Nov 16, 2011 at 14:01 | answer | added | Jonathan Kiehlmann | timeline score: 8 | |
| Nov 16, 2011 at 13:42 | history | asked | Joanna K-P | CC BY-SA 3.0 |