Timeline for Finite abelian group admits a Frobenius group of automorphism
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
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| Apr 16, 2023 at 13:58 | vote | accept | user44312 | ||
| Apr 10, 2023 at 13:28 | vote | accept | user44312 | ||
| Apr 10, 2023 at 13:28 | |||||
| Apr 10, 2023 at 12:48 | history | edited | LSpice | CC BY-SA 4.0 |
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| Apr 9, 2023 at 4:58 | answer | added | user44312 | timeline score: 1 | |
| Apr 8, 2023 at 3:56 | comment | added | user44312 | Thanks for your idea. @RichardLyons | |
| Apr 8, 2023 at 3:55 | comment | added | user44312 | Thanks for your idea. @DaveBenson | |
| Apr 7, 2023 at 15:42 | comment | added | Richard Lyons | Perhaps Harris's proof can be modified to prove something like the following. Let $A$ be a finite abelian $p$-group on which a group $X$ acts. Suppose that that for every $X$-invariant subquotient $B/C$ of $A$ (i.e., both $B$ and $C$ are $X$-invariant) such that $B/C$ is elementary abelian, $X$ acts completely reducibly on $B/C$. Then $A$ is the direct sum of $X$-invariant homocyclic subgroups. | |
| Apr 6, 2023 at 22:03 | comment | added | Dave Benson | Yes, that's right. | |
| Apr 6, 2023 at 3:49 | comment | added | user44312 | My understanding of "FH-modules in the principal block have fixed points" is: Brauer characters in principal block has the trivial Brauer character as its irreducible constituent. So, $|IBr(B_0)|=1$. Am I right? @DaveBenson | |
| Apr 6, 2023 at 2:36 | comment | added | user44312 | Thanks for your answer. Sorry, I don't understand your point. Especially, the sentences "$FH$-modules in the principal block have fixed points" and "so things tend to decompose." Could you please explain more? @DaveBenson | |
| Apr 5, 2023 at 11:18 | comment | added | Dave Benson | The problem with trying to construct an example is that if $F$ has order coprime to $p$ and $H$ is a $p$-group then $FH$-modules in the principal block have fixed points, and all non-principal blocks have defect zero, so things tend to decompose. Maybe you can turn this into a proof of something. | |
| Apr 5, 2023 at 1:37 | history | edited | user44312 | CC BY-SA 4.0 |
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| Apr 4, 2023 at 23:56 | history | edited | user44312 | CC BY-SA 4.0 |
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| Apr 4, 2023 at 16:24 | history | edited | Derek Holt | CC BY-SA 4.0 |
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| Apr 4, 2023 at 14:10 | history | asked | user44312 | CC BY-SA 4.0 |