Timeline for Is there a subgroup of a non-abelian $p$-group $G$ with a large nilpotency class?
Current License: CC BY-SA 4.0
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| when toggle format | what | by | license | comment | |
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| Sep 20, 2023 at 19:25 | history | edited | LSpice | CC BY-SA 4.0 |
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| Sep 20, 2023 at 12:41 | vote | accept | solver6 | ||
| Sep 20, 2023 at 11:15 | answer | added | YCor | timeline score: 12 | |
| Sep 20, 2023 at 10:14 | comment | added | YCor | @AchimKrause the question is whether $H$ exists for every $G$. By the way, your assertion is not true: if $H=C_p^n$, then according the action, the semidirect product $C_p^n\rtimes C_p$ can have any class between $1$ and $n$. | |
| Sep 20, 2023 at 10:14 | comment | added | Achim Krause | Ah, you're asking whether we have such $H$ for any $G$, got it. | |
| Sep 20, 2023 at 10:10 | comment | added | Achim Krause | Maybe I'm misunderstanding the question, but can't you just take abelian $H$ and $G=H\rtimes C_p$ a nontrivial semidirect product? Then $c(G)=2$ and $c(H)=1$. | |
| Sep 20, 2023 at 10:00 | history | asked | solver6 | CC BY-SA 4.0 |