I've come across some posts that said they were closed as exact duplicates, and some that were closed as duplicates.      The first image is a duplicate question and the second one is an exact duplicate.  How does a question get closed as a duplicate and how does it get closed as an exact duplicate?
On duplicate questions, I often see different headings for the duplicate question list. These include:     Possible Duplicate:    [duplicate question list]   and      This question already has an answer here:    [duplicate question list]   and more recently,     This question is an exact duplicate of:    [duplicate question list]   What decides which heading is placed before the duplicate question list?
I need to find all group homomorphisms of $S_n\to\mathbb{C}^*$ (for $n\ge2$), and also all group homomorphisms of $A_n\to\mathbb{C}^*$ (for $n\ge2$).  Someone on this site, two years ago, seems to have already asked the same question (). I understand what the questioner says there, but I don't understand it when he says:     Therefore there is exactly one $g:\mathbb{Z}/2\mathbb{Z}\to\mathbb{C}^*$, so all elements of $a\in\mathbb{C}^*$ give us $\operatorname{ord}(a)\mid g[\mathbb{Z}/2\mathbb{Z}]$, so $a$ can only be $-1$ or $1$. Now we know that $f:S_n\to\{-1,1\}$ &hellip;   What is he saying there? And how to go on from there? (I do not understand the answer given either &hellip;)  I hope that someone here can help me further. (And if I'm not allowed to ask this question because is has already been asked two years ago, please tell me what to do instead).  Thank you in advance! In Back to the Future, how did Marty get the timing right with the lightning strike? So, in the first movie, presumably the Doc and Marty know exactly when the lightning will strike the clock tower. This is because Marty has the flyer with the picture of the stopped clock on it. In order to power the DeLorean, the Doc cooks up this contraption to conduct the lightning through a hook into the DeLorean. All Marty has to do is be driving at 88 mph and hit the wire at the exact right moment.  Here's the question though - if you recall, the Doc sets a timer and tells Marty to drive back to a pre-designated starting point. When the timer goes off, Marty is supposed to accelerate to 88 mph. My assumption is that the Doc has calculated the maximum acceleration of the DeLorean, and using this value has determined the exact starting point that the car needs to be at in order to hit the lightning at the right time.  Unfortunately, the car stalls. It takes Marty a while, but he's finally able to start it up. Being that he started late though...shouldn't he have missed the lighting? 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} Sorting by "hot" - what does it mean and why are the sort option different between the homepage and the questions tab? It has come to my attention that on the homepage on any given SE you can sort by "active", "hot", "week", and "month".  The tooltip says the latter three sort by "most views, answers, and votes" over different periods of time.  So it seems that this is uses a different formula than the "arbitrary hotness points" that create hot network questions.  What is the formula and what is the rationale for using views here, but not in the network hot questions?    Also, what is the rationale for offering such different sorting options between the homepage and the questions tab?  I have been active for ~4 months and never realized there was a sort by hotness option on a different screen (as I have always looked at the questions tab to see what was new) until today. If the center of a group $G$ is of index $n$, prove that every conjugacy class has at most $n$ elements. (This question is from Dummit and Foote, page 130, 3rd edition.)  Here is my attempt: we have  $|G| =|C_G (g_i)| | G : C_G (g_i)| $  $|C_G (g_i)| =|Z(G)| \cdot  |C_G (g_i):Z(G)| $.  Then   $|G|= |Z(G)|\cdot |C_G (g_i):Z(G)|\cdot | G : C_G (g_i)| $.  Then  $n = |C_G (g_i):Z(G)|\cdot  | G : C_G (g_i)| $.  But $|C_G (g_i):Z(G)|$ is positive integar as  $ Z(G)$ is   subgroup of  $C_G (g_i)$.  If $| G : C_G (g_i)|$ bigger than $n$, then $|C_G (g_i):Z(G)|\cdot | G : C_G (g_i)|$ is bigger than $n $.  But   $|C_G (g_i):Z(G)|\cdot | G : C_G (g_i)|=n$, contradiction.  Then $| G : C_G (g_i)|\le n$ and this completes the proof.   Is this proof right or not ??!!! I'm using BibLaTeX to handle my bibliography and I want a reference to be placed in a footnote on every page where I cite the same work and have the same number. Also I want to be able to cite the same work on one page several times. The latter could be done by using  from the Joseph Wright's blog. However, it puts a reference in a footnote only once. What is the purpose of a serial number? Can non-magical persons see the Hogwarts Express during its journey to and from Hogwarts? What is the difference between independent and mutually exclusive events? How to disable pylint 'Undefined variable' error for a specific variable in a file? Why don't the Google Docs CTRL + ALT shortcuts work? I'm currently using Google Docs, but when I try to use the keyboard shortcuts like Ctrl+Alt+M it gives µ instead.    Is Chrome (9) overruling Google Docs in some way?  How can I get these shortcuts working?  I'm using Chrome dev 9 on a Dutch Windows 7 with a US-layout keyboard Is there always an equivalent metric which is not complete? How can I String.Format a TimeSpan object with a custom format in .NET? What is the recommended way of formatting TimeSpan objects into  a string with a custom format? I have problems with my Tilgin Vood Router. As I try to start my router by turning the power on (captain obvious), it generally doesn't work the first 3-4 times. This is getting very annoying.  Five minutes after turning the power on the router's signal LEDs don't blink in the way they should do in a connected state. I can connect to my routers web configuration interface through my PC connected to it via LAN though I can't access the internet.  It usually takes the router five minutes to get to the point where it should be connected to the internet but as it doesn't work the first times.  So I turn on my router 3-5 times, let him work 5 minutes and then suddenly, after turning the power off and on again it all works.  I also have to restart my PC too in order for everything to work.   How can I solve this problem? Just leave the router turned on all time? I prefer a daily IP switch, though. May the problem have something to do with my PC? There is another one connected to the router too and it doesn't work there either. Prove $ \sin(A+B)\sin(A-B)=\sin^2A-\sin^2B $ How would I verify the following double angle identity. $$ \sin(A+B)\sin(A-B)=\sin^2A-\sin^2B $$ So far I have done this. $$ (\sin A\cos B+\cos A\sin B)(\sin A\cos B-\cos A\sin B)  $$But I am not sure how to proceed. Is Checksum to file back decoding possible? So, I was having this weird thought. If the checksums(MD5 or SHA...) are unique to any file and are modified if any part of the file is edited, why cant the checksums be decoded back to get the original file? That is if I want to send a large(say 700MB) video, instead I could send just the hash and the file be decoded locally in my friend's computer. I know the thought is stupid, but is it possible by any chance? Or am I missing some thing here? And forgive me if I'm wrong, I ain't a professional. I need a non trivial  examples of group isomorphism that maps $G\to H$ such that   $G/H \cong G$. Why is homology invariant under deformation retraction/homotopy equivalence? pain of browser back button In bash, read after a pipe is not setting values