Timeline for Number of elements in $\mathrm{GL}(n,p)$ with maximal order
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| May 9, 2020 at 15:42 | review | Close votes | |||
| May 12, 2020 at 19:33 | |||||
| May 9, 2020 at 15:24 | comment | added | Geoff Robinson | The way to see this is to see that there are $\frac{\phi(p^{n}-1)}{n}$ conjugacy classes of elements of order $p^{n}-1$, and then note that if $A$ is a matrix of multiplicative order $p^{n}-1$ in $G = {\rm GL}(n,p)$, then $|C_{G}(A)| = p^{n}-1.$ | |
| May 9, 2020 at 15:21 | history | edited | YCor | CC BY-SA 4.0 |
formatting, added tags
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| May 9, 2020 at 15:18 | comment | added | Geoff Robinson | To be precise, I think the number of such matrices is $\frac{\phi(p^{n}-1)|{\rm GL}(n,p)|}{n(p^{n}-1)}$. | |
| May 9, 2020 at 15:10 | comment | added | Geoff Robinson | Rational canonical form is very relevant here. This is really a question about linear algebra and possible minimum polynomials. | |
| May 9, 2020 at 14:57 | review | First posts | |||
| May 9, 2020 at 15:22 | |||||
| May 9, 2020 at 14:47 | history | asked | Cyrius Nugier | CC BY-SA 4.0 |