Timeline for Dimension of projective cover of trivial $kG$-module
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Aug 12, 2021 at 9:49 | vote | accept | Master Gang | ||
| Aug 12, 2021 at 8:09 | answer | added | Derek Holt | timeline score: 4 | |
| Aug 12, 2021 at 5:47 | comment | added | მამუკა ჯიბლაძე | @DerekHolt May I ask which software did you use? | |
| Aug 12, 2021 at 1:25 | comment | added | Master Gang | Maybe it is appropriate for me to just ask for an counterexample. And I have editted the question to make it more clearly. | |
| Aug 12, 2021 at 1:21 | history | edited | Master Gang | CC BY-SA 4.0 |
added 71 characters in body
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| Aug 12, 2021 at 0:48 | comment | added | Master Gang | @ Geoff Robinson @ Derek Holt Thanks. I asked it since there are very little examples in my mind. I just know that it is transitive permutation group of degree less than $4p$ and has cyclic Sylow $p$-subgroups of order $p$. | |
| Aug 11, 2021 at 16:17 | comment | added | Derek Holt | You really have to provide more context with questions like this. What is the significance of the permutation representation of degree at most $4p$? Why $4p$ in particular? Why $p(p-1)$ in particular. Anyway, with a routine computer search, I found a counterexample of order $660$ with $p=3$, where the projective cover has dimension $12$. | |
| Aug 11, 2021 at 15:46 | history | edited | Geoff Robinson | CC BY-SA 4.0 |
Typo corrected
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| Aug 11, 2021 at 15:28 | history | edited | Geoff Robinson | CC BY-SA 4.0 |
typo corrected
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| Aug 11, 2021 at 15:17 | comment | added | Geoff Robinson | Why would you believe that should be true? | |
| Aug 11, 2021 at 15:03 | history | asked | Master Gang | CC BY-SA 4.0 |