It seems like there is no trivial isomorphism between them and both are abelian and non-cyclic, so, it makes it even harder to conclude anything. I need some hints.  If I had to make a guess, I'd probably say there is no isomorphism between them.
Does there exists an Isomorphism between $\mathbb{C}^* $ under multiplication with $\mathbb{C}$ under addition.  Attempt In my opinion It does not exists.  If there exists such an isomorphism say $\phi :\mathbb{C}^* \to \mathbb{C}$ then, from the fact that Isomorphism takes identity to identity we have $$\phi \left( 1 \right)=0$$  From the fact      Given $\phi:G \to H$ be an isomorphism, then For a fixed integer $k$ and a fixed group element $b$ in $G$, the   equation $x^k=b$ has the same number of solutions in $G$ as does   the equation $x^k=\phi\left(b\right)$ in $H$.   We have $x^4=1$ and $x^4=0$ must have same number of solutions, but the solutions to these equations are 4 and 1 only.
How to install with Wubi when it says "Could not retrieve the required disk image files"? I tried to install Ubuntu 12.10 with the Wubi installer while running Windows, because my PC does not accept my BootCD as a bootable medium.  But Wubi showed me this error:  Ubuntu-Installationsprogramm (X) Ein Fehler ist aufgetreten: Could not retrieve the required disk image files Weiter Informationen finden Sie in der Protokolldatei: c:\users\username\appdata\local\temp\wubi-12.10-rev273.log   What can I do, because I want to get rid of my Windows 7 and use the way better Ubuntu 12.10?  Thanks for your huge answer, now my next problem after trying to install wubi with the .iso is, that the same error shows up again and i am not shure which part of the errorreport you need.  Can you tell me? Because i'm not that good at linux. $f(z)=\frac1{2\pi i}\int_{\Gamma}\frac{f(\zeta)}{z-\zeta}d\zeta$ if $\lim_{z\to\infty}f(z)=0$ and $f$ is analytic in $|z|\ge1$ Let $f$ be analytic in $|z|\ge1$ and  $\lim_{z\to\infty}f(z)=0$. Then is $f(z)=\frac1{2\pi i}\int_{\Gamma}\frac{f(\zeta)}{z-\zeta}d\zeta$,$\forall |z|\ge2$, where $\Gamma$ is the circle of radius $2$ with centre at the origin.   I think yes, by the Cauchy integral formula. But, how do we ensure that the non analyticity of $f$ in $|z|&lt;1$ dosent affect the formula? Thanks beforehand. "invalid EFI file path" while booting Windows How can I convert an integer into its verbal representation? Is there a library or a class/function that I can use to convert an integer to it's verbal representation?  Example input:     4,567,788`   Example output:     Four million, Five hundred sixty-seven thousand, seven hundred eighty-eight Transfer from JFK Terminal 2 to Terminal 4 I have family who does not speak English.  They are changing planes in JFK Airport and will most likely be transferring from Terminal 2 (Delta) to Terminal 4 (China Southern Airlines).  At first I thought that directing them to use the Airtrain would be best.  However, in doing more reading my understanding is that the Airtrain would mean they would need to go through security again.  I found this on Delta's site:   If they use the JITNEY Shuttle to change from Terminal 2 to Terminal 4, does that mean they would not need to re-clear Security?  Edit: They are flying TO China. They are going from Tampa -> NY JFK -> China. Lower the amount of reputation needed to comment is a great example of people coming from Google and using answers as comments.  I understand the reputation threshold is there to prevent spam, but Answers are just as prone to spam as comments and you can post them at reputation 1. Furthermore there are already flags in place as a preventive measure for both.  Essentially the reputation threshold of comments is forcing people to use the site in ways the designers did not intend. Removal of the reputation cap would also make the site more new user friendly as newbies that use the site in this manner are commonly given a unfriendly welcome in the form of downvotes from people who forget you need 50 rep to post comments. When true polymorphed creature dies, does it revert to its original form? The  description says:     Creature into Creature.   The transformation lasts for the duration, or until the target drops to 0 hit points or dies. If you concentrate on this spell for the full duration, the transformation lasts until it is dispelled.   Does the second sentence imply the creature won't revert to its normal form, even being killed? (providing the caster were concentrating on the spell for the full duration)  If so, isn't "until the target drops to 0 hit points" enough? Why the "...or dies" addition? A creature can't die having more that 0 hit points, can it? I recently changed my username to Undo. I was amazed when I pressed Submit and saw that it actually went through - surely someone somewhere was using this same username.  Out of curiosity, I then search the SO user list for Undo - and found  with Undo as thier name. They have 50 rep. I have around 1,500.   Is there some kind of pecking order, I.e. a high-rep user can 'steal' a low-rep user's name? Or is this a bug?  Or can two users have the same username without causing the SO servers to go down in a burning ring of fire? How do I create an animated gif from still images (preferably with the command line)? I want make a .gif animated picture from a given set of .jpg pictures.  I would prefer to do it from the command line, so command line tools would be very welcome. Why don't custom upstart job names tab complete in the service command? How to return only the Date from a SQL Server DateTime datatype There are two syntaxes for command substitution: with dollar-parentheses and with backticks. Running top -p $(pidof init) and top -p `pidof init` gives the same output. Are these two ways of doing the same thing, or are there differences? What advantages does manual mode have over aperture priority mode? I'm wondering what are the most compelling reasons to switch to manual mode on my DSLR. I mostly just use aperture priority mode so I have good control over the depth of field combined with an awareness of the shutter speed that goes with it. My photography is mostly done wandering about with camera in hand, or occasionally on a tripod. I don't do studio photography and I just use the natural light.  I did learn how to take photos manually (with an Olympus OM-1) so I know how to do it, but I enjoy the extra convenience of aperture mode, particularly being able to take the photo quickly and capturing the moment rather than fiddling with dials and missing the shot.  So what would be some key advantages of using manual mode for my sort of photography that are worth the (small amount of) extra hassle involved?  And do you have any tips to minimise the downside (other than practicing to be quick)? How can I force SQL Server Management Studio to update the IntelliSense cache? IntelliSense in SSMS isn't updating unless I shut it down and restart. I've tried disconnecting from the server and reconnecting while the SSMS session is active, but that isn't working.  Steps to recreate:    Create a table  Select something from that table SSMS displays squiggly red lines under it with the tip "invalid object name" Execute the query   How can I force IntelliSense to update without restarting SSMS? Command-line-friendly full-text indexing? Is there such a thing as a full-text indexing engine, that can be queried from the command line and ideally wouldn't require using a gui at all ?  I'm especially interested in indexing my ebooks and papers, so that's a mixture of pdf, epub and a few djvu. (Open)Office docs would be nice, but much lower on my list. Which of the following are correct and which are wrong?   The 2000-year-old computer The 2000 year-old computer The 2000 year old computer The 2000-years-old computer The 2000 years-old computer The 2000 years old computer   In a documentary, BBC4 used the title The 2000 year-old computer, which I believe to be wrong. Am I right? Does "+" use in String concatenation affect efficiency? How do you match only valid roman numerals with a regular expression? Thinking about , i decided I can't even create a regular expression that will match roman numerals (let alone a context-free grammar that will generate them)  The problem is matching only valid roman numerals.  Eg, 990 is NOT "XM", it's "CMXC"  My problem in making the regex for this is that in order to allow or not allow certain characters, I need to look back. Let's take thousands and hundreds, for example.  I can allow M{0,2}C?M (to allow for 900, 1000, 1900, 2000, 2900 and 3000). However, If the match is on CM, I can't allow following characters to be C or D (because I'm already at 900).  How can I express this in a regex? If it's simply not expressible in a regex, is it expressible in a context-free grammar? Large braces for specifying values of variables by condition How do I produce a conditional expression with large brackets? For example: X = 0 if a=1, 1 otherwise, with a large left bracket and specifying each condition in a line? Let $p$,$\ q$ be prime numbers and $n\in \mathbb{N}$ such that $p \nmid n-1$. If $p \mid n^q-1$, then $q \mid p-1$.