Timeline for Transitive permutation groups which all of their proper subgroups are intransitive
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 15, 2016 at 19:26 | comment | added | verret | @YCor, if you mean what is the smallest degree of a transitive group with no regular subgroup, it is 6. There are five examples of degree $6$, including for example $A_6$ and (the smallest, by order) $A_4$ on 6 points. The smallest example of prime-power degree has order $32$ and degree $8$. | |
| Apr 15, 2016 at 18:28 | comment | added | YCor | Question: what's the smallest possible value of $|\Omega|$? The smallest prime power seems to be 32. | |
| Apr 15, 2016 at 17:39 | answer | added | DavidLHarden | timeline score: 3 | |
| Apr 15, 2016 at 17:14 | answer | added | YCor | timeline score: 5 | |
| Apr 15, 2016 at 2:50 | comment | added | majid arezoomand | Dear Geoff, You are right. Thank you for your comment. | |
| Apr 15, 2016 at 2:47 | vote | accept | majid arezoomand | ||
| Apr 15, 2016 at 2:46 | vote | accept | majid arezoomand | ||
| Apr 15, 2016 at 2:47 | |||||
| Apr 14, 2016 at 20:55 | answer | added | Chris Godsil | timeline score: 13 | |
| Apr 14, 2016 at 20:31 | history | edited | Stefan Kohl♦ |
Added top-level tag.
|
|
| Apr 14, 2016 at 20:29 | answer | added | Stefan Kohl♦ | timeline score: 9 | |
| Apr 14, 2016 at 20:29 | answer | added | Dima Pasechnik | timeline score: 8 | |
| Apr 14, 2016 at 19:08 | answer | added | Geoff Robinson | timeline score: 6 | |
| Apr 14, 2016 at 18:53 | comment | added | Geoff Robinson | This is just the definition of a minimal transitive group. It probably would be better to just ask for a characterization of minimal transitive subgroups of ${\rm Sym}(\Omega)$. This will depend on arithmetical properties of $|\Omega|$. So, for example, if $|\Omega| = p^{n}$ for some prime $p$ and integer $n$, then a minimal transitive group on $\Omega$ will be a $p$-group. | |
| Apr 14, 2016 at 18:43 | history | asked | majid arezoomand | CC BY-SA 3.0 |