Timeline for Automorphism-conjugacy
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Dec 10, 2022 at 7:06 | comment | added | Ville Salo | @RyleeLyman: Your answer is exactly what I was looking for, I am specifically interested in the automorphism problem. For some reason I only looked for a name of the equivalence relation, rather than searched for the problem directly. Probably this is also where I have encountered it. | |
| Dec 10, 2022 at 6:52 | comment | added | Ville Salo | I did some rewording because of the close vote, because maybe the wording was not optimal, although I don't know whether the vote was about wording or content. | |
| Dec 10, 2022 at 6:51 | history | edited | Ville Salo | CC BY-SA 4.0 |
added 329 characters in body
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| Dec 9, 2022 at 23:55 | comment | added | LSpice | Right, sorry. Actually, I only read the start of that comment, and didn't register the mention of the holomorph at the end. I will delete my comment. | |
| Dec 9, 2022 at 21:27 | comment | added | Ville Salo | @LSpice: Yes, I mentioned that above. There are many characterizations of this property. | |
| Dec 9, 2022 at 21:03 | review | Close votes | |||
| Dec 14, 2022 at 9:16 | |||||
| Dec 9, 2022 at 15:48 | comment | added | Robbie Lyman | In the context of Whitehead's algorithm for free groups, this usually goes by the name "automorphically equivalent" | |
| Dec 9, 2022 at 11:15 | comment | added | Ville Salo | I agree that this is such a simple notion that it may not need a name. Nevertheless, maybe it has one. Some that I considered are "automorphic", "automorphically conjugate", "automorphism-conjugate", "outer-conjugate" (or something in that direction), "externally/holomorphically conjugate" (the elements are conjugate in the holomorph), some being more sensible than others. I'm fine with also not having a name, but this would help look for information on this. | |
| Dec 9, 2022 at 11:11 | comment | added | Ville Salo | Yes, that's a possible roundabout way of rewording the definition. | |
| Dec 9, 2022 at 11:01 | comment | added | Carl-Fredrik Nyberg Brodda | I don't quite understand. I guess you mean that $g, f$ are fixed group elements here, and that if there is an inner automorphism $\alpha$ mapping $g$ to $f$ then we say that $g$ and $f$ are conjugate -- but what if $\alpha$ is not inner? (I think this is your question). In that case, don't we just say that $g$ and $f$ are in the same automorphic orbit? | |
| Dec 9, 2022 at 10:21 | history | edited | Martin Sleziak |
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| Dec 9, 2022 at 10:04 | history | asked | Ville Salo | CC BY-SA 4.0 |