Maximal subgroups of ${\rm PSL}(2,8)$ I’m reading  on the subgroup structure of classical subgroups. According to Corollary 2.2 (d), since $8=2^3$ is a prime power of even number $2$, ${\rm PSL}(2,8)$ has a maximal subgroup ${\rm PSL}(2,2)=S_3$. But ${\rm PSL}(2,8)$ has exactly $3$ conjugacy classes of maximal subgroups.  The three non-conjugate maximal subgroups of ${\rm PSL}(2,8)$ are $C_9\rtimes  C_2$, $C_7\rtimes C_2$ and $C_2^3\rtimes C_7$, none of which is $S_3$. I believe I misunderstood something when reading the reference, but I don’t know what that is. Could you give me some help? Any help would be appreciated.
Reference for the subgroup structure of $\rm{PSL}_2(q)$ This material is covered in detail in Dickson's "Linear Groups with an exposition of the Galois Field Theory", chapter XXII and Huppert's "Endliche Gruppen", chapter II, paragraph 8. Since I don't speak german and Dickson's treatment often requires deciphering, I was wondering if there is a "modern" account of this somewhere.
Birational map from elliptic curve keeps smoothness? Let $E$ be a elliptic curve that is , genus $1$ smooth curve with base point. And suppose that the map $φ$, which sends $E$ to $E'$, is birational. Birational means there are two rational maps on both direction which composites identity. Then, can we say that $E'$ is smooth? How can I retain HTML form field values in JSP after submitting form to Servlet? ubuntu terminal is not working properly in vi editor Compiz Problems (Plugin Missing, Performance Issues, Development) I'm using an iPhone, but I would imagine it's the same for other mobile devices as well.  If you browse to any stack exchange site, you get a very well made mobile site.  The only gripe that I have is that I can't find any way to view the number of visitors to my questions?  Am I missing something or could this possibly be integrated into the mobile renderer? Prove that the additive groups $\mathbb{R}$ and $\mathbb{Q}$ are not isomorphic. Is there a better (or other) way(s) to prove the following statement? Also, the same argument works for multiplicative groups $\mathbb{R}-\{0\}$ and $\mathbb{Q}-\{0\}$, right?       Problem Prove that the additive groups $\mathbb{R}$ and $\mathbb{Q}$ are not isomorphic.   Solution By cantor's diagonal argument, there is no possible bijection between $\mathbb{Q}$ and $\mathbb{R}$. Since an isomorphism needs to be a bijection, there is no possible isomorphism between the additive groups $\mathbb{R}$ and $\mathbb{Q}$.    Thanks Perform feature normalization before or within model validation? I have a simular issue to the question asked in :  I have tried the solution provided by Jake. This makes that my picture fails to resize (scale) as i intend.  Whether i give Set scale=0.4 or Set scale=0.8 The size of the  picture remains the same  This is the code i use:  \begin{figure}[ht!] \centering \begin{tikzpicture}[Set scale=0.4, every node/.append style={transform shape},] % STYLES \tikzstyle{every node}=[rectangle,rounded corners, minimum width=100pt,     align=center,node distance=3cm,fill=black!10,inner sep=5pt,text width=3cm,minimum height=1.75cm,&gt;=stealth,text badly centered] % Draw forces \node [force, above of=rivalry] (top) {Firm strategy, structure and rivalry}; \node [force, left=1cm of rivalry] (left) {Factor conditions}; \node [force, right=1cm of rivalry] (right) {Demand Conditions}; \node [force, below of=rivalry] (bottom) {Related and Supporting industries}; %%%%%%%%%%%%%%%% % Draw the links between forces \path[&lt;-&gt;,thick]  (left) edge (right) (left) edge (top) (left) edge (bottom) (top) edge (right) (bottom) edge (right); \path[&lt;-&gt;,thick]  (bottom) edge (top); \end{tikzpicture} \caption{Porter's Diamond source:~\cite{Porter:1980}}% \label{fig:diamond}  \end{figure} I have Ubuntu server 12.04 installed, so I have no GUI. When I do the command ifconfig, I cannot find my internal IP address. It says inet addr: 127.0.0.1. Here is the output of ifconfig -a: eth0   link encap:Ethernet  HWaddr 00:06:4f:4a:66:f0     BROADCAST MULTICAST  MTU:1500  Metric:1     RX packets:0 errors:0 dropped:0 overruns:0 frame:0     TX packets:0 errors:0 dropped:0 overruns:0 carrier:0     collisions:0 txqueuelen:1000     RX bytes:0 (0.0 B)  TX bytes:0 (0.0 B)  eth1   link encap:Ethernet  HWaddr 00:16:ec:05:c8:9c      BROADCAST MULTICAST  MTU:1500  Metric:1     RX packets:0 errors:0 dropped:0 overruns:0 frame:0     TX packets:0 errors:0 dropped:0 overruns:0 carrier:0     collisions:0 txqueuelen:1000     RX bytes:0 (0.0 B)  TX bytes:0 (0.0 B)  lo     Link encap:Local Loopback     inet addr 127.0.0.1  Mask:255.0.0.0     inet6 addr:  ::1/128 Scope:Host     UP LOOPBACK RUNNING MTU:65536  Metric:1     RX packets:1800 errors:0 dropped:0 overruns:0 frame:0     Tx packets:1800 errors:0 dropped:0 overruns:0 carrier:0     collisions:0 txqueuelen:0     RX bytes:143896 (143.b KB)  TX bytes:143896 (143.8 KB)  here are the contents of etc/network/interfaces: # The loopback network interface auto lo iface lo inet loopback  # The primary network interface auto eth0 iface eth0 inet dhcp  If someone could edit this for me, the contents of etc/network/interfaces should be on separate lines. The output of host askubuntu.com was: ;; connection timed out; no servers could be reached.  I set up owncloud and webmin a few months ago and was using them for a month with no problems. I think the power went off one day 2 months ago and I never turned the server back on until yesterday. I haven't done anything that would have affected the internet setup So i'm not sure why it doesn't work anymore. As far as my network topology goes, I have a pci-e network card for the pc. The ethernet line goes from the network card to a switch, and then to a modem/router from there. How to restrict users on changing their wallpapers? I don't want my users to change the system wallpaper. How do I the lock the wallpaper down? Update  Users are changing wallpaper by right clicking the picture and choosing set as wallpaper. How to restrict this behaviour?  Is it possible to remove Backgrounds Tab from Appearance Preferences? If yes how? How do I efficiently get "the most recent corresponding row"? I have a query pattern that must be very common, but I don't know how to write an efficient query for it.  I want to look up the rows of a table that correspond to "the most recent date not after" the rows of another table.  I have a table, inventory say, which represents the inventory I hold on a certain day.  date       | good | quantity ------------------------------ 2013-08-09 | egg  | 5 2013-08-09 | pear | 7 2013-08-02 | egg  | 1 2013-08-02 | pear | 2   and a table, "price" say, which holds the price of a good on a given day  date       | good | price -------------------------- 2013-08-07 | egg  | 120 2013-08-06 | pear | 200 2013-08-01 | egg  | 110 2013-07-30 | pear | 220   How can I efficiently get the "most recent" price for each row of the inventory table, i.e.  date       | pricing date | good | quantity | price ---------------------------------------------------- 2013-08-09 | 2013-08-07   | egg  | 5        | 120 2013-08-09 | 2013-08-06   | pear | 7        | 200 2013-08-02 | 2013-08-01   | egg  | 1        | 110 2013-08-02 | 2013-07-30   | pear | 2        | 220   I know one way of doing this:  select inventory.date, max(price.date) as pricing_date, good from inventory, price where inventory.date &gt;= price.date and inventory.good = price.good group by inventory.date, good   and then join this query again to inventory. For large tables even doing the first query (without joining again to inventory) is very slow.  However, the same problem is quickly solved if I simply use my programming language to issue one max(price.date) ... where price.date &lt;= date_of_interest ... order by price.date desc limit 1 query for each date_of_interest from the inventory table, so I know there is no computational impediment.  I would, however, prefer to solve the whole problem with a single SQL query, because it would allow me to do further SQL processing on the result of the query.  Is there a standard way to do this efficiently? It feels like it must come up often and that there should be a way to write a fast query for it.  I'm using Postgres, but an SQL-generic answer would be appreciated. Why do I need 50 reputation to comment? What can I do instead? Users with less than 50 reputation points cannot write comments on questions and answers that they don't own.  Why does this limit exist? But I want to contribute now. What should I do instead? But I can't write a good answer without more information! Shouldn't I be allowed to post comments if I have reputation on a different site? But I saw a new user posting a comment! How did they do it? Why do I need 50 reputation to comment on my own post?   See also:    in the Help Center We moved to a new place where the dryer connection is 3-prong instead of 4-prong. The dryer was originally 4-prong, so we bought a 3-prong cord and installed it. It works fine, except I am not entirely sure if I installed the ground wire correctly.   Originally, there was a green wire on the cord itself, and that was connected to the screw on the top of the first picture. This is, I assume, used to ground the case and prevent shocks when touching the exterior of the dryer.  Now with the 3-pronged plug, there is no ground wire on the cord. So where does the existing green wire in the case go? Do I leave it where it originally was like in the first picture or do I connect it to the central terminal like in the second picture?      There's no bonding strap running from the case to any terminal. I can't tell where the green wire is connected to. How do I install pillow in Ubuntu 16.04 LTS? I went to  for installing Pillow since the original PIL is a discontinued project and so now not so good to use. But, in the table support for Ubuntu 16.04 LTS is unmentioned. It appears neither in , or in .     Further, just installing pillow is said to be not enough. There are some dependencies that should be installed first which is also unmentioned for Ubuntu 16.04 LTS. Would the installation steps for Pillow for python 3 given for 14.04 LTS be OK for Ubuntu 16.04 LTS?  If not, How do I install pillow in 16.04 LTS for Python 3.6? (There is support for Python 2.) Sum of the series $1+\frac{1\cdot 3}{6}+\frac{1\cdot3\cdot5}{6\cdot8}+\cdots$ I was wondering if there is a simpler way to find the last to digits of a power such as $3^{45}$. I reduced it modulo 100 to get the answer, which is 43. But I was curious if there was a simpler, or more eloquent way to get this result.  Here's my method:  Using the fact that $3^4=81\equiv -19 \pmod{100}$ and $19^5=2,476,099\equiv -1 \pmod{100}$  $$ 3^{45}\equiv 3(3^4)^{11}\equiv 3(-19)^{11}\equiv 3(-19)(19^5)^2\equiv 3(-19)(-1)^2 \equiv -57 \equiv 43 \pmod {100} $$  I just felt like this was sort of a messy way to find out that the last two digits are 43. How do I diff two text files in Windows Powershell? I have two text files and want to find the differences between them using Windows Powershell. Is there something similar to the Unix diff tool available? Or is there another other way I haven't considered?  I've tried compare-object, but get this cryptic output:  PS C:\&gt; compare-object one.txt two.txt  InputObject                                                 SideIndicator -----------                                                 ------------- two.txt                                                     =&gt; one.txt                                                     &lt;= Ability to give away iOS application, usually for sale I am wondering if it's possible to do "mass giveaways" on the AppStore, without lowering, changing or otherwise changing the listed application.  Is it possible to distribute hundreds to, potentially, thousands of promo codes, legally, while still leaving the "normal" distribution channel of purchasing the app open?  An example of the above would be selling physical items in a store which have a bundled digital component available. Essentially you buy a product in a store, which comes "bundles with a free app" (BB and Android have already been dealt with, iOS is unclear). It would be nice to give the option to have a promo code in the box, that the user can then use to get the application for free. Is this possible? Does going outside of range or line of sight after casting a spell have any effect? Does going outside the range of the spell or breaking line of sight between the caster and target break concentration or otherwise affect control over the spell?  For example, a Heat Metal spell has a range of 60 ft. If I cast the Heat Metal spell on a an armored foe, and that foe runs outside the range of the spell (60 ft), or around the corner, does that break concentration and end the spell? Heat Metal also allows you to use a bonus action to cause the 2d8 of damage — would exercising that option be prevented by being out of range or line of sight? Texture is missing in Cycles? Because I am pretty new to blender I watched the tutorial  from BlenderCookie.com.  I loaded  onto a sphere but then in all views the texture is just some kind of blurry with no details.