Timeline for Finite simple groups with three conjugacy classes of maximal local subgroups
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Aug 22, 2020 at 8:41 | comment | added | Geoff Robinson | @LSpice: ${\rm PSL}(2,2^{q})$ is just the same as ${\rm SL}(2,2^{q})$. As you say, the centre of the latter group is trivial, so this is consistent notation, but with some redundancy in this case. | |
| Aug 21, 2020 at 22:30 | comment | added | LSpice | You twice referred to $\operatorname{PSL}(2, 2^q)$ "for some prime $p$", which I think was meant to be "… for some prime $q$"; I edited accordingly, as well as some other small changes. (Also, what does $\operatorname{PSL}(2, 2^q)$ mean? I would normally think that you are taking the quotient by the centre, but it's trivial ….) | |
| Aug 21, 2020 at 22:28 | history | edited | LSpice | CC BY-SA 4.0 |
Link to article; \DeclareMathOperator; prime p -> prime q
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| Aug 21, 2020 at 19:02 | answer | added | Geoff Robinson | timeline score: 2 | |
| Aug 21, 2020 at 13:50 | comment | added | Derek Holt | Yes, the three classes of maximals subgroups of ${\rm PSL}(2,2^q)$ with $q$ prime consist of dihedral groups of orders $2(2^q \pm 1)$, and a group with structure $2^2:(2^q-1)$, and all of these are local. But there are other simple groups, such as $A_6$ and ${\rm PSL}(2,16)$, with exactly three classes of maximal subgroups that are local. I am afraid that finding them all would involve a lot of hard work on your part! | |
| Aug 21, 2020 at 12:55 | history | edited | YCor | CC BY-SA 4.0 |
fixed question
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| Aug 21, 2020 at 12:51 | review | First posts | |||
| Aug 21, 2020 at 14:28 | |||||
| Aug 21, 2020 at 12:49 | history | asked | Benedict | CC BY-SA 4.0 |