Let $G$ be a group of order $399$. Then by Sylow, it must have a normal subgroup of order $19$, denoted by $H$. Let $N, K$ be groups of order $7$ and $3$. Then $HN$ and $HK$ are groups of order $133$ and $57$. What is the possible order of their normalizer?  The normalizer can only be either themselves or the whole group by Lagrang
Here's a question I've been asked;  Given distinct primes $p,q,r$, show that any group $G$ of order $pqr$ is not simple.   So far, my idea has been to individually check each possible proper subgroup, since by Lagrange there are only $$\dbinom{3}{2} + \dbinom{3}{1} + 1$$ of them, and show that at least one of them other than the trivial group is normal. Surely there is a smarter way, since generalizing this approach wouldn't work so well if I wanted to show similar results for groups who's order is a product of $n$ distinct primes.  Is there some other approach? Thanks for any insights
What is the geometric meaning of the determinant of a matrix? I know that "The determinant of a matrix represents the area of ​​a rectangle." Perhaps this phrase is imprecise, but I would like to know something more, please.  Thank you very much. Why does the following code sometimes causes an Exception with the contents "CLIPBRD_E_CANT_OPEN":  Clipboard.SetText(str);   This usually occurs the first time the Clipboard is used in the application and not after that. What is the difference between Interest Rate and APY on savings accounts, CDs, etc?  Is there a simple formula to convert the two? how to run the dialog command with proccess Please look on my code – ( bash script )  I want to display both dialogs on the screen on the same time,   one dialog display the:  tail –f from - /var/log/proccess1.log  ,   and the second dialog display the:  tail –f from the file - /var/log/proccess2.log     but the sad fact is that I can display only one dialog and not both dialogs ( because when I run the first dialog , the second dialog will activate only if the first dialog will killed )   So I create process on the second dialog ( ….. ) &amp;    , in order to display both dialogs    But …. the second dialog create process number but not create the second dialog GUI , ( seems that when we create dialog with process , the process not send the dialog to standard output )  So how to  run the second dialog with process but send the dialog GUI to screen ? , or other solution in order to display both dialogs on screen  My code       #!/bin/bash       # this dialog will locate the tail box on the top of the screen      dialog --begin 15 10  --tailbox   /var/log/proccess1.log  13 125         # this dialog will locate the tail box down in the screen      ( dialog --begin 37 10  --tailbox   /var/log/proccess2.log    13 125 ) &amp; Change bend angle and swap node position on arrow How did Thanos know about the power of "The Snap"? In the scene on Titan with Doctor Strange in Avengers: Infinity War, Thanos said,     With all six Infinity Stones, I will simply snap my fingers and it would all cease to exist.   Then again, in the very first scene with Thor and Loki, when Maw gave Thanos the Space Stone, he said that no one has ever worn two Infinity Stones together.   So how come Thanos knew about the power of the Snap? Because as Wong puts it to Tony, the Big Bang hurled the six Infinity Stones across the universe.   So if no one had collected all the six stones before Thanos, then how did he know about the ability to "Snap"? Suppose $G$ is a group generated by elements $x$ and $y$ where $xy^2 = y^3x$ and $yx^3 = x^2y$ What can you prove about $G$? Suppose $G$ is a group generated by elements $x$ and $y$ where $xy^2 = y^3x$ and $yx^3 = x^2y$ What can you prove about $G$?  I've just been playing around with the relations but I can't seem to get anywhere. It seems as if I'm going in circles. I don't know what to look for in terms of how the equations should look in order to give me an insight into the structure of the group.  So given a group presentation, are there any general strategies of what to look for in the relations (as in how to rearrange them) in order to obtain insight about the group? Install on Second Hard Drive with startup boot option? In theory, what I want to do is very simple, but I've done some google research and read some posts on this site and I'm still confused.   I want to keep win7 on my primary C:\ drive, and install Ubuntu (12.10) on a secondary drive (that I have yet to buy or install. I just want to be certain that I'm successful when I do this). If at all possible I'd also like it if when I start the computer I have the option to boot either Win7 or Ubuntu, like an account log in type thing where I just pick which drive I'm running with that day. And just to reiterate, I do not want to partition my C:\ drive or alter, change, or affect my Win7 system in any way.  The reason I'm still fairly uncertain about all of this, is that a lot of the guides I've read have been for earlier versions of Ubuntu. Also the vast majority of guides are about partitioning one drive to fit both OS'. I want two separate OS running from two separate drives that I can pick at boot. The guides I did find mentioned that there is some issue with the grub being installed on C:\ but the rest of the OS being installed on the other drive. Is this still the case? How do I avoid that?  Also, if it helps, I've been running 12.04lts on my laptop for a few months now in and out of class and I love it.  Finally, if you could please point me to a guide or write your answer in the form of a guide for a two year old that'd be awesome. I'm still an Ubuntu novice and I don't want to mess up my win7. How do I share an ethernet connection via wifi on Windows 8? I have a Windows 8 laptop that is connected to a router via Ethernet. I want to make the laptop act like a wireless router via wifi so that other devices could connect to the computer using wifi and gain access to its Ethernet internet connection.  How do I do something like this? How to generate multiple maps where one highlighted attribute changes? I have a layer that contains counties within the state of Washington.    I need to build one map (jpg) for each county.  For that specific map all counties will show as light grey, but the specific county will be green, and the file name will be the county name. If I have a shapefile or geodatabase featureclass that has fields that I want to permanently reorder, is there a tool, script, or utility that will help me quickly accomplish this task? Generally I know you have to create a new field, then populate it with the old values, then delete the old field.  I am hoping there is something already created out there that will help with this. Assuming you don't have FME or another ETL tool available, what is the next best suggestion? This is NOT a view level change (ie- drag/drop the fields in order), but rather write out to a new shapefile or featureclass. Event handler not working on dynamic content Determining true mean from noisy observations How to stop Katoolin from crashing Ubuntu? I want to hit enemy's axe to break it. How this is properly played in D&amp;D 5e? And what about shield or armor? Can I attack these items to break it? I'm trying to remove some characters from file(UTF-8). I'm using tr for this purpose:   tr -cs '[[:alpha:][:space:]]' ' ' &lt;testdata.dat    File contains some foreign characters (like "Латвийская" or "àé"). tr doesn't seem to understand them: it treats them as non-alpha and removes too.  I've tried changing some of my locale settings:  LC_CTYPE=C LC_COLLATE=C tr -cs '[[:alpha:][:space:]]' ' ' &lt;testdata.dat LC_CTYPE=ru_RU.UTF-8 LC_COLLATE=C tr -cs '[[:alpha:][:space:]]' ' ' &lt;testdata.dat LC_CTYPE=ru_RU.UTF-8 LC_COLLATE=ru_RU.UTF-8 tr -cs '[[:alpha:][:space:]]' ' ' &lt;testdata.dat   Unfortunately, none of these worked.  How can I make tr understand Unicode? How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$? How can one prove the statement $$\lim_{x\to 0}\frac{\sin x}x=1$$ without using the Taylor series of $\sin$, $\cos$ and $\tan$? Best would be a geometrical solution.  This is homework. In my math class, we are about to prove that $\sin$ is continuous. We found out, that proving the above statement is enough for proving the continuity of $\sin$, but I can't find out how. Any help is appreciated. How soon can I re-enter the USA having stayed for 90 days under the Visa Waiver Program? I am currently visiting the USA from the UK (I am a UK citizen) and am intending on staying here for the full 90 days under the Visa Waiver Program.     How long would I have to stay out of the US at the end of this period before returning again?    Would I have to return to the UK, or could I stay with friends in another country (such as Canada) for a while? Looking for a quick and dirty way to automate . I presume this could be done with an automation to press the mouse button from two separate pixel coordinates, with delay, so long as the browser window doesn't move -- unless there's a better way.  I tried building a Watch Me Do workflow, in Automator, but can't seem to get it to work.  I get the error "application Chrome is not running when it is expected to." It also never lists mouse clicks for some reason.  I do have accessibility set up, in system preferences > security &amp; privacy > privacy > accessibility.  Automator, Chrome and System Events are all checked within there (among other stuff of course).  I tried the markashworth workaround as detailed  -- which also doesn't seem to work. Using his method, I get this error:    UPDATE: I just downloaded "cliclick" and figured out how do both clicks as a terminal command, with the proper delays.  BUT -- I don't know code and need a way for this terminal command to repeat "x" amount of times.  Anyone know how I could do that in Script Editor?  The command line is:  cliclick c:132,286 w:100 c:132,286 w:5000 c:1100,238   I would need a few seconds of delay before the loop repeats, which I presume I could do with a final "w:" in that line.  Thanks for the help!! Essentially, I would like to set my phone so that all my outgoing messages to a specific friend, with whom I currently text back and forth over iMessage, are sent out over SMS, never iMessage. Additionally, I would like to block any incoming iMessage texts of his and (hopefully) they'll fail and be resent via SMS.  Let me restate that: I would like to force SMS for both parties, going both ways, for a specific individual contact.   Is this possible? Blocking any usage of iMessage between myself and this other individual, so they must either send and receive any texts to or from me via SMS (or the texts fail/never arrive).