Timeline for Perfect group that is split extension of a normal free subgroup of finite index
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 24, 2022 at 7:53 | comment | added | IJL | @YCor: great idea to get it down to $F_4$. | |
| May 24, 2022 at 0:02 | vote | accept | tota | ||
| May 24, 2022 at 0:02 | |||||
| May 23, 2022 at 16:38 | comment | added | tota | Thanks@IJL for your answer. | |
| May 23, 2022 at 16:27 | comment | added | YCor | And I guess the smallest $F_n$ we can thus get is indeed $F_4$, since every finite subgroup of $\mathrm{Aut}(F_n)$ for $n\le 3$ is solvable. | |
| May 23, 2022 at 16:26 | comment | added | YCor | Nice. If instead of the free product $A_5\ast A_5$ you take the double $A_5\ast_{A_4}A_5$, you still have a canonical split surjection onto $A_5$, and this time, by the same argument, you get $F_4=F_{5-1}$ as kernel (as you get 5 free orbits instead of 60 free orbits of edges). | |
| May 23, 2022 at 15:06 | history | edited | IJL | CC BY-SA 4.0 |
added 531 characters in body
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| May 23, 2022 at 14:58 | history | answered | IJL | CC BY-SA 4.0 |