Timeline for Rational cohomological dimension of a locally finite group
Current License: CC BY-SA 4.0
14 events
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| Sep 24, 2021 at 11:00 | comment | added | Benjamin Steinberg | @YCor, in Derek's paper or seemed to conjecture at least n. Maybe Derek will chime in. | |
| Sep 24, 2021 at 7:22 | comment | added | YCor | Browsing subsequent papers (see other papers by Holt in 1981 and those quoting him, etc), there seems to be a few more papers on this, but I'm not sure what they exactly conjecture or say (as it doesn't only focus on rational cd, and also because some make set-theoretic assumptions). Does it conjecture that a locally finite group of cardinal $\aleph_n$ has rational cohomological dimension $n$, and infinite when $n\ge\aleph_0$? Is part of the conjecture known (e.g., is it known that the cohomological dimension is $\ge n$? is it known for abelian groups? etc. | |
| Sep 24, 2021 at 1:42 | vote | accept | Linda | ||
| Sep 23, 2021 at 21:14 | history | edited | YCor | CC BY-SA 4.0 |
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| Sep 23, 2021 at 21:03 | history | edited | Benjamin Steinberg | CC BY-SA 4.0 |
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| Sep 23, 2021 at 20:36 | comment | added | Benjamin Steinberg | @YCor, he shows H^2 is not zero when G is uncountable | |
| Sep 23, 2021 at 20:35 | history | edited | Benjamin Steinberg | CC BY-SA 4.0 |
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| Sep 23, 2021 at 19:25 | comment | added | YCor | There's one thing I know making a big difference between countable and uncountable locally finite groups: $H^1(G,\mathbf{Z}G)$ is infinite when $G$ is infinite countable locally finite, while it's zero for $G$ locally finite uncountable. This former (easy) fact is due to Scott-Sonneborn; the latter is due du Holt. | |
| Sep 23, 2021 at 19:21 | history | edited | Benjamin Steinberg | CC BY-SA 4.0 |
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| Sep 23, 2021 at 19:17 | history | edited | Benjamin Steinberg | CC BY-SA 4.0 |
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| Sep 23, 2021 at 19:11 | history | edited | Benjamin Steinberg | CC BY-SA 4.0 |
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| Sep 23, 2021 at 19:05 | history | edited | Benjamin Steinberg | CC BY-SA 4.0 |
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| Sep 23, 2021 at 18:49 | history | edited | Benjamin Steinberg | CC BY-SA 4.0 |
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| Sep 23, 2021 at 18:27 | history | answered | Benjamin Steinberg | CC BY-SA 4.0 |