I am reviewing for a test and i find the following good exercice. Would you please help me to prove the second part of the question b) here   for question a) i find $|G|=32$ since $G=C_8\ltimes C_2\times C_2$ Thanks for your help in advance.
Please help me to prove the following result:  I recall that the holomorph $Hol(\Gamma)$ of a group $\Gamma$ is the semidirect product $Hol(\Gamma)=\Gamma\ltimes_{\phi} Aut(\Gamma)$ where $\phi: Aut(\Gamma)\to  Aut(\Gamma)$ is the identity map.  Let $G=Hol(C_8)$. In addition let $f(x)\in \mathbb{Q}[x]$ be an irreducible polynomial of degree $8$, $L$ a splitting field of $f(x)$ over $\mathbb{Q}$ and suppose that $Gal(L/\mathbb{Q})\cong G$     Show that there is a subgroup of $S_8$ isomorphic to $G$   Thanks in advance.
Why do we make a distinction between derivatives and partial derivatives? I want to install the PyCharm IDE by JetBrains for Python (free community edition).  I managed to , but I do not know how to install it. Can you please help me? Cannot see OpenLayers under Plugin in QGIS? Although I have installed the OpenLayers plugin in QGIS 2.4, I cannot see it in the list when I click on Plugins.    Does anyone else have this issue? What is the C# equivalent of friend? Possible Duplicate:          I'd like the private member variables of a class to be accessible to a Tester class without exposing them to other classes.   In C++ I'd just declare the Tester class as a friend, how do I do this in C#? Can someone give me an example? Custom 500 Error page: Is there a way to theme a fatal error? In /core/includes/errors.inc, when there is a fatal error it outputs a response with the message "The website encountered an unexpected error. Please try again later." and a back-trace, if error_level is set to verbose, and without the back-trace otherwise.  It seems like at this point, there's no way, with an event subscriber to capture the response and alter it.  Is that correct?  Or is there a way to wrap the output from line 268 of errors.inc in Drupal 8.4 with markup?    Note, there's another , but that doesn't offer a complete solution.  Also, I looked into .htaccess and Apache ErrorDocument directive, but that . Once Apache passes off to PHP, it can no longer use that directive.  That's for real server errors. Infectious chicken pox My 21 year old son has chicken pox and has been home for a few days now. The spots are just starting to crust over.  I work with elderly people but have had chicken pox as a child - should I carry on working while he is here (hes usually away at Uni) and infectious? I am trying get an unused server up and running, it booted fine but i was greeted with the login window and none of the known passwords seem to work. The server I am trying to get to work is not a Domain Controller and has not been used in a long time.  OS: Windows 2003 Server R2 Enterprise Edition  I tried Ophcrack XP (there is no WinServer version of Ophcrack) - it couldn't locate the partitions with hashes. I tried mounting the partitions myself (#mount /dev/hda*x* /mnt/ntfs), but it gave me an error saying /dev/hda*x* didn't exist.  Next I tried booting into a Ubuntu 10.04.3 LiveCD so that I could install and use chntpw - no go, Ubuntu Live wouldn't boot.  Based on what I've read up the following tools may be of help:   Windows Password recovery Petter Nordahl-Hagen's Offline NT Password &amp; Registry Editor Openwall's John the Ripper EBCD – Emergency Boot CD - Bootable CD (R)ecovery (I)s (P)ossible Linux rescue system   I am hoping that someone here has prior experience with Win2k3 Administrator password resets so that I don't end up having to try all of the above to find out which one works. Many-worlds: how often is the split how many are the universes? (And how do you model this mathematically.) Let's consider two statements: Zorn's lemma and theorem about existence of maximal ideals in commutative ring with $1$.  It's easy to prove that Zorn's lemma implies existence of maximal ideals.  I wonder if the converse proposition is true, i. e., does existence of maximal ideals implies Zorn's lemma? My approach was to construct a ring structure on an ordered set which satisfies Zorn's lemma condition such that existence of maximal ideal implies existence of maximal element in the set, but I didn't succeed. Show that $A_n=\sum\limits_{k=1}^n \sin k $ is bounded? What does the Web.Config file do in the views folder of a MVC project Does the Polyjuice Potion Dark Mark work? I was just reading Harry Potter and the Deathly Hallows, and I was wondering, when Hermione Granger changed into Bellatrix Lestrange, she should've obtained the Dark Mark, temporarily.  Now, my question is: would the Dark Mark work if pressed? I know how to use the subfig package to fit many subfigures (each with its own caption) into a larger figure (with a general caption).  I know how to use the sidecap package, the put a figure's caption on the side of the figure.  What I do not know is how to display a caption inside the figure, as if it were a subfigure.  More precisely, I have three subfigures that I would like to fit on a 2x2 layout, with the remaining quadrant used for the caption.    Is that easy to achieve? What is the difference between lands and mana? What is the relationship between lands and mana in Magic and what do each of them do?  A good answer should especially include how a new player should think about them.    Note:  This is an attempt to create a canonical question about the relationship between lands and mana in Magic.  Beginners are often confused about this given the same symbols are used to mean different things across basic lands, non-basic lands, and mana costs.  This can lead to confusion about , about , or even about . I found it in an old dictionary and I'm not sure what it means. It looks like the number &quot;3&quot;, but the top of the three has been flattened(and slightly curved). I've only seen this in three or four words. [] MySQL Query GROUP BY day / month / year Why is the present perfect used in headlines? In news reports, we often read or hear events introduced with the present perfect, and then the past simple like this:     The film star Jim Cooper has died of cancer. He was 68 and lived in Texas.   What's wrong if we use both first and second sentence in past simple?     The film star Jim Cooper died of cancer. He was 68 and lived in Texas. Can't install Skype 4.3 on Ubuntu 14.04 64 bit First of all, I think this question is not duplicated, because I have tried all other solutions I found here, but nothing solved my problem.  I use Ubuntu 14.04 64 bit.  I have tried until now: sudo apt-get install skype -> It didn't work. The error was:   The following packages have unmet dependencies: skype : Depends: skype-bin E: Unable to correct problems, you have held broken packages.   I have tried sudo dpkg add-architecture &amp;&amp; sudo dpkg -i skype-ubuntu-precise_4.3.0.37-1_i386.deb but it didn't work either. The error was:  dpkg: dependency problems prevent configuration of skype: skype depends on libqt4-dbus (&gt;= 4:4.5.3); however: Package libqt4-dbus is not installed. skype depends on libqt4-network (&gt;= 4:4.8.0); however: Package libqt4-network:i386 is not installed. skype depends on libqt4-xml (&gt;= 4:4.5.3); however: Package libqt4-xml:i386 is not installed. skype depends on libqtcore4 (&gt;= 4:4.7.0~beta1); however: Package libqtcore4:i386 is not installed. skype depends on libqtgui4 (&gt;= 4:4.8.0); however: Package libqtgui4:i386 is not installed. skype depends on libqtwebkit4 (&gt;= 2.2~2011week36); however: skype depends on libstdc++6 (&gt;= 4.2.1); however: Package libstdc++6:i386 is not installed. skype depends on libx11-6; however: Package libx11-6:i386 is not installed. skype depends on libxext6; however: Package libxext6:i386 is not installed. skype depends on libxss1; however: Package libxss1:i386 is not installed. skype depends on libxv1; however: Package libxv1:i386 is not installed. skype depends on dpkg: error processing package skype (--install): dependency problems - leaving unconfigured Processing triggers for hicolor-icon-theme (0.13-1) ... Processing triggers for gnome-menus (3.10.1-0ubuntu2) ... Processing triggers for desktop-file-utils (0.22-1ubuntu1) ... Processing triggers for bamfdaemon (0.5.1+14.04.20140409-0ubuntu1) ... Rebuilding /usr/share/applications/bamf-2.index... Processing triggers for mime-support (3.54ubuntu1) ... Errors were encountered while processing: skype   I have tried to use after sudo apt-get -f install but it didn't solve the issue.  I have tried to install by using Gdebi. The error was:  Cannot install 'libqtwebkit4:i386'   I have tried to install using Ubuntu Software Center. The error was:  Cannot install 'libqtwebkit4:i386'   I have tried changing the server in "Software and Updates". I have tried to use "Main Server" and "Servers for United States". But it couldn't solve my problem.  Anyone has any idea how to solve that?  SOLVED  Well, I formatted my pc and I installed Skype first of all. Probably another installation that I had done before the Skype installation was the problem, i guess.  Thanks people! How should I setup separate MX records for a subdomain? In eevee, shadows are clipped by camera distance As shown in the gif, the shadow in eevee is clipped by the camera distance. The same is true for F12 rendering. Where are the options to improve this issue?