Timeline for How many minimum generating sets are there in a finite group?
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Nov 10, 2023 at 9:50 | comment | added | Emil Jeřábek | Similar question: mathoverflow.net/questions/248037/… | |
| Nov 19, 2019 at 17:00 | vote | accept | CommunityBot | ||
| Aug 31, 2019 at 17:52 | answer | added | Luc Guyot | timeline score: 2 | |
| Aug 27, 2019 at 9:02 | comment | added | YCor | It's very unclear what is asked. What is the infimum over all groups of order $n$ of the number of minimum generating subset? What's a procedure for a given group (in which case there's no reason to introduce $n$ in the question)? Anyway "Is there a known lower bound?": yes, 1 is a known lower bound. | |
| Aug 27, 2019 at 8:59 | history | edited | YCor | CC BY-SA 4.0 |
clarified, removed useless definition of equality and added needed definition of minimum
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| Aug 27, 2019 at 8:50 | answer | added | Geoff Robinson | timeline score: 5 | |
| Aug 27, 2019 at 7:47 | comment | added | user108347 | minimum generating set means minimum number of elements that generates $G$. | |
| Aug 27, 2019 at 4:18 | comment | added | user108347 | I am interested in minimum generating sets not minimal generating sets. | |
| Aug 26, 2019 at 16:24 | comment | added | Gerhard Paseman | Can anything be said about minimal sets beyond Tarskis Basis Theorem? Gerhard "Wonders About Universality Of Problem" Paseman, 2019.08.26. | |
| Aug 26, 2019 at 15:09 | comment | added | LeechLattice | The point is that there're lots of nonisomorphic minimum generating sets. For example, two random elements from $A_n$ almost surely generate $A_n$ for $n→+\infty$, so the bound is nearly $|A_n|^2$. | |
| Aug 26, 2019 at 15:07 | comment | added | user108347 | @ Bullet51 Every nonabelian finite simple group is has a generating set of size 2. | |
| Aug 26, 2019 at 15:04 | comment | added | LeechLattice | Are there any restrictions on $G$? Things could be much more different if $G$ is a simple group. | |
| Aug 26, 2019 at 10:15 | comment | added | LeechLattice | Inspired by @GeoffRobinson's comment, here's a more general bound: $|\text{Aut}G|/k!$, where $k$ is the size of the minimum generating set. | |
| Aug 26, 2019 at 9:24 | history | asked | user108347 | CC BY-SA 4.0 |