Timeline for Agemo-of-agemo inclusions for p-groups
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Aug 28, 2023 at 8:17 | comment | added | grok |
It has order $2^{167}$, and can be produced in GAP with the commands LoadPackage("anupq"); and Pq(FreeGroup(2):Prime:=2,ClassBound:=8);
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| Aug 25, 2023 at 12:13 | comment | added | YCor | I indeed understood incorrectly as I often used $k$-nilpotent to mean $k$-step-nilpotent. OK, I understand now (that's "8-step-(2-nilpotent)" in some sense). This is a quite big group then, what's its order? | |
| Aug 25, 2023 at 10:29 | comment | added | grok | No, you understood correctly: the $2$-nilpotent refers to the prime $2$, while $8$ is the class. Start with $G_1=F$ the free group on $2$ generators, and define $G_{i+1}=[G_i,F]\mho_1(G_i)$. I did the calculations in $F/G_8$. | |
| Aug 24, 2023 at 13:32 | comment | added | YCor | However I did the calculation on the free 2-step-nilpotent exponent-8 group on 2 generators (which has order $2^8$) and it seems to me that both $\mho_1(\mho_2(G))$ and $\mho_2(\mho_1(G))$ are trivial therein. I might have misunderstood something. | |
| Aug 24, 2023 at 8:48 | comment | added | YCor | Class 8: you mean exponent 8? Class usually refers to nilpotency class (which is 2 here). | |
| Aug 24, 2023 at 8:45 | history | answered | grok | CC BY-SA 4.0 |