Timeline for Estimating the cardinality of the set of conjugacy classes of subgroups in a finite group of given order
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Mar 18 at 15:20 | comment | added | Mikhail Borovoi | @GeoffRobinson: Many-many thanks! | |
| Mar 18 at 15:14 | comment | added | Geoff Robinson | The theorem mentioned in that answer is by Borovik, Pyber and Shalev. My own answer to that question is more informative than my comments above. | |
| Mar 18 at 15:09 | comment | added | Geoff Robinson | The relevant question is mathoverflow.net/questions/132675 . The answers/comments there include references to Pyber's result. | |
| Mar 18 at 14:37 | comment | added | Mikhail Borovoi | @GeoffRobinson: Concerning László Pyber, do you remember the title, or a word from the title, of the corresponding paper? | |
| Mar 18 at 14:34 | comment | added | Mikhail Borovoi | Thank you for your prompt comment, @GeoffRobinson! A stupid question: what is the number of subgroups for the elementary Abelian $2$-group of order $n=2^r$ ? | |
| Mar 18 at 14:18 | comment | added | Geoff Robinson | You probably can't do better than $n^{c\log{n}}$ for some constant $c$, as an elementary Abelian $2$-group of order $n = 2^{r}$ illustrates. I think I have answered questions like this before, but I could not find them. I think L. Pyber might have shown that this sort of bound is asymptotically optimal. By the way, the difference between "number of subgroups" and "number of conjugacy class of subgroups" is probably negligible, since they differ by a factor at most $n$. | |
| Mar 18 at 14:02 | history | asked | Mikhail Borovoi | CC BY-SA 4.0 |