Timeline for On the iterated automorphism groups of the cyclic groups
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 4, 2020 at 15:07 | comment | added | Sebastien Palcoux | Do you think we can translate Q5 into a purely number theoretic problem? | |
| Jan 31, 2020 at 20:39 | comment | added | Derek Holt | There are several related posts on this issue, such as this one and this one. But I am not aware of any known example in which the orders of the groups in the chain of automorphism groups of a finite group have been proved to be unbounded. | |
| Jan 31, 2020 at 14:09 | comment | added | Sebastien Palcoux | @GeoffRobinson: and what about the existence of a finite group $G$ for which ${\rm Aut}^{n}(G)$ does not stabilize? Any known cyclic group example? Derek's example $C_{341}$ is a candidate, but it is known? Is there a finite group $G$ whose sequence ${\rm Aut}^{n}(G)$ is (for $n$ large enough) periodic non-constant? | |
| Jan 31, 2020 at 12:19 | comment | added | Sebastien Palcoux | @DerekHolt Is it known whether, for a given finite group $G$, $Aut^n(G)$ is constant for $n$ large enough? | |
| Jan 31, 2020 at 11:32 | comment | added | Sebastien Palcoux | Q1 asks for a classification of the set $\{Aut^m(C_n) \ | \ n>0,m \ge 0 \}$ (up to equivalence). This set could be easy to describe "negatively", in the sense that it could be all the finite groups except a tractable list. | |
| Jan 31, 2020 at 10:24 | history | edited | Geoff Robinson | CC BY-SA 4.0 |
Minor correction/clarification
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| Jan 31, 2020 at 9:58 | comment | added | Derek Holt | I just tried some computations with $n=11 \times 31$, and the orders of the series of automorphism groups seem to be increasing rapidly, starting $300$, $5760$, $46080$, $566231040$. | |
| Jan 31, 2020 at 9:50 | history | answered | Geoff Robinson | CC BY-SA 4.0 |