Timeline for Checking for a normal p-complement with a computer
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Apr 27, 2023 at 14:00 | comment | added | Derek Holt | @DavidA.Craven Computing normal closure is polynomial time and fast in Magma. For general $O^\pi(G)$ that looks to be a good way to do it. For normal $p$-complements there is not much difference in performance between doing that and computing the lower central series, particularly when combined with Geoff's quick method for getting a negative answer. | |
| Apr 26, 2023 at 11:57 | comment | added | David A. Craven | For constructing the $O^\pi(G)$, does the algorithm that sets $H=1$, choose a $\pi'$-elements at random, add to $H$, then take normal closure until $|G:H|$ is a $\pi$-number, work fast? Not sure how fast the normal closure algorithm is. $O^\pi(G)$ and $O_\pi(G)$ should be native commands in Magma, definitely. | |
| Apr 24, 2023 at 18:15 | vote | accept | Mare | ||
| Apr 24, 2023 at 18:15 | comment | added | Mare | Thanks. Magma is much faster than expected, even for such large groups. | |
| Apr 23, 2023 at 16:18 | history | edited | Derek Holt | CC BY-SA 4.0 |
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| Apr 22, 2023 at 19:02 | comment | added | Carl-Fredrik Nyberg Brodda | Oh, of course, I was in the GAP mindset. (Which, I suppose, works as a second answer) | |
| Apr 22, 2023 at 13:25 | history | edited | Derek Holt | CC BY-SA 4.0 |
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| Apr 22, 2023 at 13:24 | comment | added | Derek Holt | @Carl-FredrikNybergBrodda In fact $\mathtt{Sylow}$ exists as an abbreviation for $\mathtt{SylowSubgroup}$ in Magma, but I will edit it anyway to make it clearer. | |
| Apr 22, 2023 at 12:36 | comment | added | Carl-Fredrik Nyberg Brodda | Should the second part not be $\texttt{IsNormal(G, SylowSubgroup(G,3))}$? Or perhaps you are using a package with a $\texttt{Sylow}$-function? | |
| Apr 22, 2023 at 11:42 | history | answered | Derek Holt | CC BY-SA 4.0 |