Timeline for Order of a rational function on $\mathbb{F}_p$
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Mar 9, 2022 at 11:51 | vote | accept | Thibault Décoppet | ||
| Mar 9, 2022 at 11:51 | history | edited | Thibault Décoppet | CC BY-SA 4.0 |
deleted 40 characters in body
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| Mar 9, 2022 at 6:20 | history | edited | Thibault Décoppet | CC BY-SA 4.0 |
added 125 characters in body
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| Mar 8, 2022 at 19:31 | answer | added | LSpice | timeline score: 7 | |
| Mar 8, 2022 at 19:25 | comment | added | David E Speyer | I think there is a sign error and you mean $\tfrac{x+a}{x+1}$? The group of Mobius transformation is isomorphic to $PGL_2(F_p)$; your transformation corresponds to $\begin{bmatrix} 1&-a \\ 1&1 \end{bmatrix}$, with characteristic polynomial $t^2 - 2 t + (a+1)$. The discriminant of this polynomial is $-4a$. The order of a matrix in $PGL_2$ divides $p+1$ if the discriminant of the char. poly. is nonsquare. It seems likely that you mean to get $4a$, so that this criterion would apply. (Even then, though, I doubt the order will be $p+1$, it will probably just divide $p+1$.) | |
| Mar 8, 2022 at 19:25 | comment | added | Kevin Casto | Maybe obvious, but this is just asking what the order of $\pmatrix{1 & -a \\ 1 & 1}$ is in $PGL(2,\mathbb{F}_p)$ | |
| Mar 8, 2022 at 19:14 | history | asked | Thibault Décoppet | CC BY-SA 4.0 |