Timeline for Maximal subgroups of special linear groups over finite fields
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 28, 2015 at 17:02 | comment | added | Derek Holt | IIf $q=p^e$, then it is at least $2e$ when $q$ is even and at least $2e+1$ when $q$ is odd. | |
| Sep 28, 2015 at 16:57 | comment | added | Derek Holt | But that's a completely different question, so its should not be asked as a comment. | |
| Sep 28, 2015 at 15:44 | comment | added | Pablo | @DerekHolt as I have indicated twice in my last comment, I am now interested in arbitrary (NOT maximal) subgroups. I appreciate your help a lot. Thanks! | |
| Sep 28, 2015 at 15:03 | comment | added | Pablo | @DerekHolt This is great! My questions regarding maximal subgroups are now settled. If I want to find a (not necessarily maximal) subgroup $H \leq \mathrm{SL}_3(\mathbb{F}_p)$ with highest rank possible. Which one should I take? | |
| Sep 28, 2015 at 14:45 | comment | added | Derek Holt | Chapter 8 containing the tables was designed to be readable independently of the rest of the book (and we suspected that most readers would probably only look at Chapter 8), so you only need look at Chapter 8. All of the subgroups are 2-generated except for $(q-1)^2:S_3$, which required $3$ generators when $q \equiv 1 \bmod 3$. Calculating the indices in $G$ should be routine. I am, happy to answer specific questions on particular subgroups. | |
| Sep 28, 2015 at 12:46 | comment | added | Pablo | @DerekHolt Sadly enough, I am still having trouble with extracting the information I need from the tables - It seems that I will have to go through the whole book if I want to follow the notation. All I want is to know (at least roughly) the ranks of the maximal subgroups. I am really glad to see that a classification exists (this is my first question) but I would also like to have an answer for my second question: "I am interested in the indices of these subgroups in $G$ and in their ranks (minimal cardinality of a generating set)." | |
| Sep 28, 2015 at 11:23 | vote | accept | Pablo | ||
| Sep 28, 2015 at 11:23 | comment | added | Igor Rivin | Sad to say, it IS available. I won't say there, to safeguard your sales, but it is not hard to find. | |
| Sep 28, 2015 at 11:22 | vote | accept | Pablo | ||
| Sep 28, 2015 at 11:23 | |||||
| Sep 28, 2015 at 10:51 | history | answered | Derek Holt | CC BY-SA 3.0 |