Timeline for Finite groups with small God's numbers
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 10, 2018 at 7:27 | answer | added | M. Farrokhi D. G. | timeline score: 7 | |
| Jul 9, 2018 at 20:17 | answer | added | Seva | timeline score: 1 | |
| Jul 9, 2018 at 14:03 | comment | added | Dirk | Intuitively I would say that you will find such a set $S$ for most groups, yes. You might be interested in this conjecture here ( en.wikipedia.org/wiki/Diameter_(group_theory) ), stating that $N(S,G)$ remains small no matter what set $S$ you take, at least as long as $G$ is simple. | |
| Jul 9, 2018 at 12:32 | comment | added | Johannes Hahn | One example that comes to mind are the Coxeter groups. For example for $G=S_n$ with S=the neighbour-transpositions the length of the longest element (the permutation $(1,n)(2,n-1)...$) is $\frac{n(n-1)}{2}=O(n^2)$, but the order of the group is of course $n! \gg n^2$ | |
| Jul 9, 2018 at 12:32 | comment | added | LeechLattice | Computing the quantity $N(S,G)$ is hard in general. The GAP package may be useful for your purpose. | |
| Jul 9, 2018 at 12:20 | comment | added | LSpice | I can imagine an asymptotic meaning, but how do I decide for a single group $G$ and generating set $S$ whether $\lvert S\rvert, N(S, G) \ll \lvert G\rvert$ is true? | |
| Jul 9, 2018 at 12:18 | comment | added | LeechLattice | Isn't that the diameter of the Cayley graph? | |
| S Jul 9, 2018 at 11:46 | history | suggested | Ali Taghavi |
I add a tag.
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| Jul 9, 2018 at 11:43 | review | Suggested edits | |||
| S Jul 9, 2018 at 11:46 | |||||
| Jul 9, 2018 at 11:35 | review | First posts | |||
| Jul 9, 2018 at 11:41 | |||||
| Jul 9, 2018 at 11:34 | history | asked | Logikus | CC BY-SA 4.0 |