Timeline for On the average number of subgroups per conjugacy class
Current License: CC BY-SA 3.0
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| S May 5, 2017 at 18:40 | history | bounty ended | CommunityBot | ||
| S May 5, 2017 at 18:40 | history | notice removed | CommunityBot | ||
| S Apr 27, 2017 at 17:03 | history | bounty started | the_fox | ||
| S Apr 27, 2017 at 17:03 | history | notice added | the_fox | Canonical answer required | |
| Apr 25, 2017 at 16:09 | history | edited | the_fox | CC BY-SA 3.0 |
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| Apr 25, 2017 at 16:04 | history | edited | the_fox | CC BY-SA 3.0 |
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| Apr 25, 2017 at 15:48 | history | edited | the_fox | CC BY-SA 3.0 |
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| Apr 25, 2017 at 15:40 | history | edited | the_fox | CC BY-SA 3.0 |
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| Apr 25, 2017 at 15:33 | history | edited | the_fox | CC BY-SA 3.0 |
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| Apr 25, 2017 at 12:38 | comment | added | the_fox | Your suggestion to use Burnside is good; I hadn't thought of that. I think that it might be useful to try to answer the following: if $G=[N]H$ is a semidirect product of the normal $N$ with $H$, where $\gcd(|N|,|H|)=1$, is $r(G)$ related to $r(G/N)$, $r(H)$ in a "nice way"? | |
| Apr 25, 2017 at 12:20 | comment | added | the_fox | In the past, I had searched for results related to $s(G)$ or $c(G)$, but I did not find much of interest there... | |
| Apr 25, 2017 at 12:11 | comment | added | Derek Holt | On the other hand, it is possible that this problem has been studied already, so you should try and ascertain that before working too hard on it! | |
| Apr 25, 2017 at 12:09 | comment | added | Derek Holt | I am not aware of any known results in this area, but my guess is that it would be possible to prove something similar to $(*)$ with some work. For $(*)$ to fail there would have to be subgroups with normalizers of size smaller than $8$, which is possible, but has consequences on the structure of $G$. For example, if there is a self-normalizing subgroup of order $2$ or $3$, then $G$ has a normal $2$- or $3$-complement by Burnside's Transfer Theorem. | |
| Apr 25, 2017 at 11:50 | comment | added | Benjamin Steinberg | mathoverflow.net/questions/132675/… might be relevant. | |
| Apr 25, 2017 at 10:46 | history | asked | the_fox | CC BY-SA 3.0 |