Timeline for On the number of structure of $F_p[G]$-modules
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 22, 2021 at 9:12 | history | edited | gmvh | CC BY-SA 4.0 |
TeXified title
|
| Aug 18, 2020 at 19:53 | comment | added | Antoine Labelle | @Nourddine Snanou Group representations of group $G$ over a field $K$ are the same as $K[G]$-modules and this is exaftly what representation theory studies. In your case $K$ is $\mathbb{F}_p$ and $G\cong (\mathbb{Z}/p\mathbb{Z})^2$. Since the characteristic of $K$ divides $|G|$, Maschke's theorem does not hold, so this is more precisely a question of modular representation theory. I don't know much about modular representation theory, though, so I can't help you more. | |
| Aug 18, 2020 at 19:32 | history | edited | Nourddine Snanou |
edited tags
|
|
| Aug 17, 2020 at 16:49 | comment | added | Nourddine Snanou | Yes, exactly. Thank you for your clarification. Can you explain why that is a question in representation theory. Are there similar questions in representation theory. | |
| Aug 17, 2020 at 15:53 | answer | added | Derek Holt | timeline score: 5 | |
| Aug 17, 2020 at 7:24 | comment | added | Derek Holt | Dos this question have anything to do with group extensions? You seem to be just asking for the number of isomorphism classes of ${\mathbb F}_pG$-modules over ${\mathbb F}_p$, where $G$ is elementary abelian of order $p^2$. That is a question in representation theory. | |
| Aug 17, 2020 at 5:23 | comment | added | Qiaochu Yuan | @Antoine: the conjugation action of $E$ on $A$ factors through $G$ because $A$ is abelian. | |
| Aug 17, 2020 at 2:16 | comment | added | Antoine Labelle | I don't see how the extension gives to $A$ a $G$-module structure. How do you define the action of $G$? | |
| Aug 17, 2020 at 1:35 | history | edited | Nourddine Snanou | CC BY-SA 4.0 |
deleted 1 character in body
|
| Aug 17, 2020 at 1:22 | history | asked | Nourddine Snanou | CC BY-SA 4.0 |