Timeline for Infinite vertex-transitive graph where every automorphism has a fixed vertex
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Apr 20, 2022 at 12:35 | answer | added | Michael Giudici | timeline score: 6 | |
| Apr 20, 2022 at 9:17 | history | edited | YCor |
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| Apr 20, 2022 at 8:29 | comment | added | YCor | Comment on connectedness (I first thought you forgot to assume connectedness): if the graph is not connected, then using a fixed-point-free permutation of the set of components, there's a fixed-point-free automorphism. So a graph answering the question has to be connected. | |
| Apr 19, 2022 at 22:23 | comment | added | YCor | yes, sorry: "every conjugacy class of $G$ meets $C$" (actually in a singleton) | |
| Apr 19, 2022 at 20:52 | comment | added | Sam Hopkins | @YCor: presumably that's a typo for "... every conjugacy class of $G$ meets $C$"? | |
| Apr 19, 2022 at 20:46 | comment | added | YCor | Ivanov (see math.stackexchange.com/a/2147305/35400) constructed f.g. groups $G$ of prime exponent $p$ (for some prime $p$) with a cyclic subgroup $C$ of order $p$ such that every conjugacy class of $G$ meets $G$. Choose a Cayley-Abels graph $X$ for $G/C$. Then every element of $G$ fixes a point in $X$. So this would work, provided the automorphism group of $X$ is reduced to $G$. I'd guess it's possible to ensure this. | |
| Apr 19, 2022 at 18:43 | history | asked | Sam Hopkins | CC BY-SA 4.0 |