Timeline for Iterated automorphism groups of finite groups
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 30, 2019 at 13:21 | comment | added | Justin Benfield | Decided to do the center check myself, $Aut^8(G)$ has center $C_2$, so the question remains open for $C_{41}$. | |
| Nov 30, 2019 at 12:51 | comment | added | Justin Benfield | The group, $Aut^3 (C_{41})$ is not $D_4$, but a group of order 192 (with GAP Small Groups Library id of 1493 for groups of that order). I got as far as $Aut^8$, but could not verify stabilization by that step (it may be worth test if the group or any of its predecessors are centerless as then Wielandt's classic 1939 theorem would give stabilization in finitely many steps). All examples I have worked on (every group of order<64) has either stabilized or blown up beyond what I can compute in GAP. So periodic behavior would be the most surprising to see. | |
| Mar 2, 2018 at 18:03 | comment | added | Adam P. Goucher | @JoelDavidHamkins It's finite, so it may as well be given as a Cayley table. | |
| Mar 2, 2018 at 14:03 | comment | added | Nick Gill | Another relevant question: math.stackexchange.com/questions/1096939/… | |
| Mar 2, 2018 at 13:09 | comment | added | Joel David Hamkins | For your last question, in what form do you want the finite group to be given? If only as a presentation, then one can do this just by considering that the question of whether a given presentation is the trivial group or not is Turing equivalent to the halting problem. | |
| Mar 2, 2018 at 12:34 | history | asked | Adam P. Goucher | CC BY-SA 3.0 |