Timeline for Sequence of epimorphisms of residually finite groups stabilizes
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Jan 24, 2021 at 23:44 | comment | added | markvs | The proof uses only the fact that an HNN extension of a finite group is virtually free. That was known long ago (the 60s?). The argument about lamplighter groups appeared in print in arxiv.org/pdf/1206.2072.pdf, a year later than the question in MO.I am not sure there were papers containing that result before 2012. | |
| Jan 24, 2021 at 22:13 | comment | added | YCor | What I said at that question is that every (infinite locally finite)-by-finite finitely generated group is an inductive limit of a sequence of non-injective epimorphisms of virtually free finitely generated groups. It's a straightforward consequence of the 1978 Bieri–Strebel paper. However, I believe it was never said explicitly before a few years ago. | |
| Jan 24, 2021 at 20:22 | vote | accept | frafour | ||
| Jan 24, 2021 at 20:06 | history | edited | markvs | CC BY-SA 4.0 |
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| Jan 24, 2021 at 20:04 | comment | added | markvs | See the proof in the answer by YCor in the linked question. Of course it is not the original proof, | |
| Jan 24, 2021 at 19:45 | comment | added | frafour | Do you have a reference? I saw it mentioned in one of the comments of the question you cite but it does not say where it comes from | |
| Jan 24, 2021 at 17:45 | comment | added | markvs | It is the inductive limit in the standard terminology. | |
| Jan 24, 2021 at 17:16 | comment | added | Jeremy Rickard | Ah, OK! The limit here is actually a colimit in category theoretic terminology? | |
| Jan 24, 2021 at 16:29 | history | answered | markvs | CC BY-SA 4.0 |