Timeline for A "simpler" description of the automorphism group of the lamplighter group
Current License: CC BY-SA 4.0
7 events
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| Jul 17, 2023 at 17:44 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title
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| Jul 13, 2023 at 15:00 | history | became hot network question | |||
| Jul 13, 2023 at 12:28 | comment | added | AGenevois | You can take a look at Proposition 4.8 in arxiv:2110.09822. (But the result was known before, see the references given there. This is just an elementary proof.) | |
| Jul 13, 2023 at 12:08 | answer | added | Luc Guyot | timeline score: 10 | |
| Jul 13, 2023 at 9:28 | comment | added | HenrikRüping | Here are jsut some thoughts. The lamplighter group has a unique maximal torsion subgroup $Q$ and thus $Q$ is characteristic. Any automorphism maps $t$ to an element of the form $q t^{\pm 1}$ with $q\in Q$; and any such choice can be extended by $id_Q$ to an automorphism of the lamplighter group. Thus the automorphisms fixing q are given by $P\rtimes C_2$, where the action is given by inverting group elements. | |
| Jul 13, 2023 at 7:18 | history | edited | Emil Jeřábek | CC BY-SA 4.0 |
fix links
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| Jul 13, 2023 at 6:59 | history | asked | ghc1997 | CC BY-SA 4.0 |