Timeline for Is there anything known about the lower central series of a group $G\wr C_p$?
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Mar 11, 2023 at 11:43 | comment | added | Gillyweeds | Yes, indeed, it is not required. | |
| Mar 10, 2023 at 19:51 | comment | added | LSpice | Since you don't seem to use any particular embedding $G \to S_{p^m}$, it's not necessary to state it, right?—since the bare existence of such an embedding follows from Cayley's theorem, with $p^m = \lvert G\rvert$. | |
| Mar 10, 2023 at 19:50 | history | edited | LSpice | CC BY-SA 4.0 |
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| Mar 8, 2023 at 18:18 | vote | accept | Gillyweeds | ||
| Mar 7, 2023 at 16:24 | answer | added | Sean Eberhard | timeline score: 2 | |
| Mar 7, 2023 at 15:43 | comment | added | Sean Eberhard | I think my previous comment is only correct if $G$ actually elementary abelian. | |
| Mar 7, 2023 at 9:36 | comment | added | Sean Eberhard | Sorry, I missed the condition that $G$ is a $p$-group. | |
| Mar 6, 2023 at 15:47 | comment | added | Gillyweeds | Thank you very much! But in my case, $G$ is a $p$-group and $C_p$ to. What I mean is that both of the groups are powers of the same $p$, so the case $C_3\wr C_2$ is not considered. In fact it can be seen that $W(G)$ is always nilpotent, in my case. | |
| Mar 6, 2023 at 15:25 | comment | added | Sean Eberhard | The case in which $G$ is an abelian $p$-group is already not quite trivial, and it was studied implicitly by Hall in the last section of doi.org/10.1017/S0305004100031662. In this case the indices are $|G|p, |G|, |G|, \dots, |G|$. If $G$ is not a $p$-group then $W(G)$ need not be nilpotent, e.g., $C_3 \wr C_2 \cong C_3 \times S_3$ (but your question is still reasonable). | |
| S Mar 6, 2023 at 14:19 | review | First questions | |||
| Mar 6, 2023 at 14:28 | |||||
| S Mar 6, 2023 at 14:19 | history | asked | Gillyweeds | CC BY-SA 4.0 |