Timeline for Splitting of a finite group with no abelian subfactor in composition series
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Aug 5 at 8:48 | comment | added | Derek Holt | @Rami It's the proof of Theorem 1 | |
| Aug 5 at 8:42 | comment | added | Rami | @Derek Holt. Thank you very much. Can you say where in the paper it is constructed? | |
| Aug 4 at 17:04 | comment | added | Derek Holt | @Rami I didn't explain the construction of $E$, I just referred to the old paper of mine. No, the twisted wreath product in the paper you refer to is split. You will notice that the construction of the example in my post does not satisfy the assumption $(*)$ in the paper, and results in a non-split version of the twisted wreath product. | |
| Aug 4 at 14:08 | comment | added | Rami | Hi, I did not understand the construction of E. Is this the notion of twisted wreath product described here: sciencedirect.com/science/article/pii/0021869367900294is section 2? Thanks a lot | |
| Oct 7, 2022 at 10:40 | vote | accept | User01 | ||
| Sep 14, 2022 at 8:38 | history | edited | Derek Holt | CC BY-SA 4.0 |
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| Sep 14, 2022 at 8:38 | comment | added | spin | In my comment my vague intuition came from extensions of modules, where you know that if $V$ is a $K[G]$-module for a group $G$ and $\operatorname{Ext}^1(W,Z) = 0$ for all composition factors $W,Z$ of $V$, then $V$ is completely reducible. But as this answer shows that kind of stuff doesn't work for extensions of groups. | |
| Sep 14, 2022 at 7:59 | history | answered | Derek Holt | CC BY-SA 4.0 |