Timeline for Help understanding a group
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 11, 2013 at 3:40 | vote | accept | Thomas | ||
| Sep 9, 2013 at 2:52 | comment | added | Thomas | It is really surprising how many times one of the relations is redundant. For example, the added relation to make 2^3.PSL(2,7) makes the (aba,b)^6 relation redundant. | |
| Sep 7, 2013 at 4:50 | comment | added | Thomas | Thanks! I was trying to complete the list of quotients of this group. I now have PSL(2,13)-PSL(2,7)-2^6, PSL(2,13)-PSL(2,7)-2^3, PSL(2,13)-PSL(2,7), PSL(2,13), PSL(2,7)-2^6, PSL(2,7)-2^3, PSL(2,7), and the trivial group. Did I miss any out? | |
| Sep 6, 2013 at 16:26 | comment | added | Tim Dokchitser | Ah, sorry, I thought you wanted $PSL(2,13)$. Then (this is one element) $ ab^{-1}ababab^{-1}ab^{-1}abab^{-1}ababab^{-1}abab^{-1}abab^{-1}$ $ ab^{-1}abab^{-1}abab^{-1}ab^{-1}abab^{-1}ab^{-1}abab^{-1}ab $ $ ab^{-1} ababab^{-1}abab^{-1}abab^{-1}ab^{-1}abab^{-1}ab^{-1}abab $ | |
| Sep 6, 2013 at 13:44 | comment | added | Thomas | Ok, but what is the relation that will give the group with composition factors PSL(2,13)-PSL(2,7)-2^3? | |
| Sep 6, 2013 at 12:08 | comment | added | Derek Holt | Adding $[a,b]^7$ gives ${\rm PSL}(2,13)$. Adding $(ab^{-1}abab^{-1}ababab^{-1})^3$ gives one of the $2^3.{\rm PSL}(2,7)$ images. | |
| Sep 6, 2013 at 11:01 | comment | added | Tim Dokchitser | $[a,b]^7$ I think | |
| Sep 6, 2013 at 8:40 | comment | added | Thomas | Could you give a relation to add to make such a group? | |
| Sep 6, 2013 at 8:38 | comment | added | Derek Holt | Yes there are two such quotients. The group is a direct product of ${\rm PSL}(2,13)$ with a group with structure $2^{3+3}.{\rm PSL}(2,7)$. | |
| Sep 6, 2013 at 8:08 | comment | added | Thomas | Out of curiosity, is there a quotient with composition series: PSL(2,13)-PSL(2,7)-2^3? | |
| Sep 6, 2013 at 7:46 | comment | added | Thomas | Right, of course. It is interesting, there isn't a group 2^6.PSL(2,13) (at least as a quotient of the group). | |
| Sep 6, 2013 at 7:41 | comment | added | Derek Holt | Alternatively, if you run the LowIndexSubgroups command (up to index 14 is enough) then you can quickly find quotients isomorphic to ${\rm PSL}(2,13)$ and $2^6.{\rm PSL}(2,7)$ as coset images of the subgroups of low index. | |
| Sep 6, 2013 at 5:44 | history | answered | Thomas | CC BY-SA 3.0 |