Timeline for Ends of finitely generated torsion groups
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Apr 7, 2019 at 20:08 | answer | added | AGenevois | timeline score: 12 | |
| Apr 7, 2019 at 18:22 | vote | accept | Taras Banakh | ||
| Apr 7, 2019 at 11:54 | answer | added | NWMT | timeline score: 5 | |
| Apr 6, 2019 at 16:16 | comment | added | YCor | All these references are given in the introduction to arxiv.org/abs/1901.11073 (whose emphasis is on space of ends of $\infty$-ended infinitely generated groups, which can fail to be Cantor). | |
| Apr 6, 2019 at 14:45 | history | edited | Taras Banakh | CC BY-SA 4.0 |
deleted 9 characters in body
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| Apr 6, 2019 at 14:44 | comment | added | Taras Banakh | @YCor Thank you very much for the comments. Could you write them as an answer (with precise coordinates of the Freudenthal paper) and I will accept it as an answer? | |
| Apr 6, 2019 at 14:39 | comment | added | YCor | More specifically, Freudenthal (1944) observed that if a f.g. group $G$ has a space of ends $E$ with $|E|\ge 3$ then there exists a clopen subset $X$ of $E$ and $g\in G$ such that $gX$ is a proper subset of $X$. This clearly implies that $g$ has infinite order. | |
| Apr 6, 2019 at 14:34 | comment | added | YCor | The theorem you attribute to Stallings is due to Hopf and Freudenthal in 1943/44; more precisely they proved that if a f.g. group has $\ge 3$ ends then its space of ends is a Cantor space. It's also a theorem of Freudenthal (1944) that f.g. torsion groups are $\le 1$-ended (basically he proved that $\infty$-ended groups act as convergence groups on their boundary). Of course this also follows from Stallings' (genuine) later theorem ($\sim 1969$). | |
| Apr 6, 2019 at 13:32 | history | edited | Taras Banakh | CC BY-SA 4.0 |
edited title
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| Apr 6, 2019 at 13:23 | history | asked | Taras Banakh | CC BY-SA 4.0 |