I think this might be a trick question, even if it is I am still not sure how to write it.  Let G be a group  Let H be a subgroup of G  I wish to show that if $|G:H|=n$ with $n&gt;1$ then G has a quotient (or factor to some) group $G/N$ which is isomorphic to a subgroup $I$ of the Symmetric group $S_n$ with $|I|&gt;1$  I'm not actually sure what N is, I think it is a typo for H. If it is supposed to be H then (this is the bit I am not sure how to write)  I want to say something like $|G:H|$ is the number of left cosets of H in G, and the quotient group is just the group of them, if that group is of order N then of course it is isomorphic to a subgroup of the symmetric group on n items, the symmetric group contains every group as a subgroup we could have on n things.  If $N$ is intended, this usually denotes a normal subgroup, I am not sure how to interpret the question.  If you can interpret this correctly please do say how you interpreted it, hints are great when you are stuck on the question, not reading the question.  I don't think my "of course it is isomorphic to a subgroup" is the answer, it is from the wrong chapter's part (Rings Fields and Groups) to be so trivial.
If H is a subgroup of G ( | G:H |=n, n > 1), then how can you show that G has a factor group G/N which is isomorphic to a subgroup D of the symmetric group Sn with |D| > 1.  I've been looking at Cayley's Theorem but it's not specific to the factor groups.
Can you use the /testfor command in minecraft 1.8 to find out if a player has died ?  I need it for my map, where 2 players (Only) are pitted against eachother. I want it so that when one of them dies, it will detect the death and declare the victor. I'm considering re-designing my personal website to promote my web services in my local area.  My issue is whether to do a one page website with a scroll-to navigation system. What effect does this have on SEO. As i understand it, you set stuff like h1's and meta description on specific page content. How does this work when all of your different content is on one page? Why can't Discovery's Data Core be separated from the ship? I have just installed Ubuntu on my pc. Everything is working fine but the Wifi is not working properly When i am trying to connect to a network it is not working and showing error "Activation of Network Connection failed ". Sometime i am able to connect to the network but the network strength is very week. My PC uses realtek driver for wifi.  Here's the output of lspci; lsusb      00:00.0 Host bridge: Intel Corporation Atom/Celeron/Pentium Processor x5-E8000/J3xxx/N3xxx Series SoC Transaction Register (rev 21) 00:02.0 VGA compatible controller: Intel Corporation Atom/Celeron/Pentium Processor x5-E8000/J3xxx/N3xxx Integrated Graphics Controller (rev 21) 00:13.0 SATA controller: Intel Corporation Atom/Celeron/Pentium Processor x5-E8000/J3xxx/N3xxx Series SATA Controller (rev 21) 00:14.0 USB controller: Intel Corporation Atom/Celeron/Pentium Processor x5-E8000/J3xxx/N3xxx Series USB xHCI Controller (rev 21) 00:1a.0 Encryption controller: Intel Corporation Atom/Celeron/Pentium Processor x5-E8000/J3xxx/N3xxx Series Trusted Execution Engine (rev 21) 00:1b.0 Audio device: Intel Corporation Atom/Celeron/Pentium Processor x5-E8000/J3xxx/N3xxx Series High Definition Audio Controller (rev 21) 00:1c.0 PCI bridge: Intel Corporation Atom/Celeron/Pentium Processor x5-E8000/J3xxx/N3xxx Series PCI Express Port #1 (rev 21) 00:1c.1 PCI bridge: Intel Corporation Atom/Celeron/Pentium Processor x5-E8000/J3xxx/N3xxx Series PCI Express Port #2 (rev 21) 00:1f.0 ISA bridge: Intel Corporation Atom/Celeron/Pentium Processor x5-E8000/J3xxx/N3xxx Series PCU (rev 21) 00:1f.3 SMBus: Intel Corporation Atom/Celeron/Pentium Processor x5-E8000/J3xxx/N3xxx SMBus Controller (rev 21) Bus 002 Device 001: ID 1d6b:0003 Linux Foundation 3.0 root hub Bus 001 Device 006: ID 5986:065e Acer, Inc  Bus 001 Device 005: ID 0bda:b720 Realtek Semiconductor Corp.  Bus 001 Device 004: ID 046d:c077 Logitech, Inc. M105 Optical Mouse Bus 001 Device 003: ID 1c4f:0002 SiGma Micro Keyboard TRACER Gamma Ivory Bus 001 Device 008: ID 2717:ff80   Bus 001 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub   output of usb-devices | awk '/b720/' RS=  T:  Bus=01 Lev=01 Prnt=01 Port=03 Cnt=04 Dev#=  5 Spd=480 MxCh= 0 D:  Ver= 2.10 Cls=ef(misc ) Sub=02 Prot=01 MxPS=64 #Cfgs=  1 P:  Vendor=0bda ProdID=b720 Rev=02.00 S:  Manufacturer=Realtek S:  Product=802.11n WLAN Adapter S:  SerialNumber=00e04c000001 C:  #Ifs= 3 Cfg#= 1 Atr=e0 MxPwr=500mA I:  If#= 0 Alt= 0 #EPs= 3 Cls=e0(wlcon) Sub=01 Prot=01 Driver=btusb I:  If#= 1 Alt= 0 #EPs= 2 Cls=e0(wlcon) Sub=01 Prot=01 Driver=btusb I:  If#= 2 Alt= 0 #EPs= 6 Cls=ff(vend.) Sub=ff Prot=ff Driver=rtl8xxxu   How to fix this issue?? How could Thranduil have met a dragon? Get rid of the question ban on Meta; suspend actively harmful users manually appears to have been question banned because of two unpopular Meta suggestions. (He says so in )  Look at the two contributions that appear to have gotten him banned. Like those of many others, they may not be of perfect quality, but they are not actively harmful to the site, either. As it stands, you can get question blocked on Meta simply for asking questions that aren't popular with the Meta crowd.  Why does the team insist on keeping the question ban active on Meta?  Why can't real problem users be dealt with through manual moderator action? Don't tell me it's a problem of scale; as far as I can see, actually toxic users are very rare on Meta.  People will frequently complain that Meta actively discourages the expression of unpopular viewpoints and suggestions. With the threat of question bans in place, I find those complaints difficult to refute. I hate that. Spin or rotate an image on hover Get names of all keys in the collection Let $f:\mathbb{R}\rightarrow \mathbb{R}$ be continuous.Let $t\in\mathbb{R}$. Evaluate:$\lim_{h\rightarrow0}\frac{1}{h}\int_{t-h}^{t+h}f(s)ds$ So I know I've heard this saying in American English before but I just can't quite find the original.  I have come up with several made up variations like:   I don't send the Navy (or whole army, or a battalion) when all you need is a diplomat. Don't buy the whole cow when all you need is milk.   What's the more commonly heard saying/phrase for this of expression? How to Create a Half-Turn Staircase? I would like to create a half-turn staircase without a landing. Is there an easy way to accomplish this without having to manually calculate and create each step individually?  Here’s an image similar to what I would like to achive:    I have found the Archimesh add-on including . While I can bend the created stairs, I haven’t found any way to get anywhere close to the image above. My stairs just always look out of shape and I don’t know how to get the outline of the staircase into a square.  I should mention that I only have very little experience with Blender modeling, so it’s well possible that I’m just missing some curve modification basics. Perhaps Archimesh is also the wrong approach for this in the first place? How do file permissions work? I was surprised recently to find that it's possible to have a return statement in a finally block in Java.  It seems like lots of people think it's a bad thing to do as described in ''. Scratching a little deeper, I also found '' which shows some pretty horrible examples of other types of flow control in finally blocks.  So, my question is, can anyone give me an example where a return statement (or other flow control) in a finally block produces better / more readable code? How to build a dmg Mac OS X file (on a non-Mac platform)? Is it possible to build a .dmg file (for distributing apps) from a non-Mac platform? And if yes, how? Operation 'Split, All The Metas!' Shall Commence On April 16, 2014 Update 2014-04-17 04:47 UTC: Stable, with some odds and ends to clean up      The main MSO/MSE sites are stable, but there are plenty of corners left to sweep. For details, see:    Not all of them mind you, just Meta Stack Overflow into Meta Stack Exchange.  I'll have you know, factually, that we really did believe this would take place in six-to-eight weeks when it was , but we've finally got a tentative date established.  If things go according to plan, we'll begin the operation shortly after 8:30 PM EDT on the 16th, completing everything within a few hour window. Ideally, all service disrupting endeavors will be completed within the first hour, which include:   The availability of Meta Stack Overflow The availability of Stack Overflow (more on this shortly) The availability of Chat on Meta Stack Overflow   As you know, we'll be bolting on a standard issue per-site meta on Stack Overflow, while breaking the link between what will have become Meta Stack Exchange and Stack Overflow. There's some irritable innards in that particular region, so we'll be asking folks to expect the unexpected during the maintenance window. Affected sites will be in and out of read-only mode, or quite possibly just down for maintenance while we're doing the actual break.  I'll be posting a system message on both Meta Stack Overflow as well as Stack Overflow itself 24 hours before we begin the actual work.   Did I say tentative in a six-to-eight-something time frame again? Why yes, I did - we're currently running some tests on the dev tier to simulate the split as closely as possible, so that we can better anticipate quirks that we need to address prior to actually doing it.  Once the sites have actually been stood up functionally on the production tier, we're going to get to work on finishing touches. This will include things like site settings (which determine bits of text you see in the question prompts, rep thresholds, etc) and all sorts of other fine tuning.  Once we're done:   Stack Overflow will have a blank, empty child meta site just like every other site The new Meta Stack Exchange will be up and running All rooms on Chat Meta Stack Overflow will be moved to Chat Meta Stack Exchange  I'll send over about 150 - 200 questions from MSE to MSO, most of which will be tag or SO-specific feature related posts that got buried by the network stuff without resolution.   If the tentative date moves, I'll update this post with the new date. However, we do not anticipate this happening any later than Saturday, April 19 - in the case that we see down time we can't mitigate and need to do it on a weekend.  The ground work is basically done, we're finishing up sanity now with a great deal of confidence, and we're pretty certain that we'll hit between those dates, if not directly on the tentative 16th.  Questions? Kvetch? Anonymous confessions? Answer below, and I'll address each in comments. Prove that $C\exp(x)$ is the only set of functions for which $f(x) = f'(x)$ Community, please show some holiday spirit! Why does ? And more importantly: why does she not wear them?    Please, show some goddamn holiday spirit! Can we get Community to wear her hats, either randomly or through popular vote? I have a conjecture that any two positive coprime integers $a$ and $b$ can be added to form any integer greater than or equal to $(a-1)(b-1)$.   This is true for $3$ and $5$, which can form any integer greater than or equal to $8$, where $8=3+5, 9=3+3+3, 10=5+5; k=3n+8$ or $3n+9$ or $3n+10$.  It is true for $4$ and $7$, which can form any integer greater than or equal to $18$, where $18=4+7+7, 19=4+4+4+7, 20=4+4+4+4+4, 21=7+7+7$, etc. How can it be proven that this will work for any two coprime numbers? Invert Color Ramp in QGIS I have no idea how to prove it by using only what the book has talked about so far. Can anyone help? The proof shouldn't be using set theory as set theory is only mentioned in the following chapter. The proof should only make use of the addition of natural numbers, order properties of natural numbers, the trichotomy of order for natural numbers and principle of induction.  Proposition 2.2.14 (Strong principle of induction). Let $m_0$ be a natural number, and let $P(m)$ be a property pertaining to an arbitrary natural number $m$. Suppose that for each $m ≥ m_0$, we have the following implication: if $P(m')$ is true for all natural numbers $m_0 ≤ m' &lt; m$, then $P(m)$ is also true. (In particular, this means that $P(m_0)$ is true, since in this case the hypothesis is vacuous.) Then we can conclude that $P(m)$ is true for all natural numbers $m ≥ m_0$. Exercise 2.2.5. Prove Proposition 2.2.14. (Hint: define $Q(n)$ to be the property that $P(m)$ is true for all $m_0 ≤ m &lt; n$; note that $Q(n)$ is vacuously true when $n &lt; m_0$.)  Thanks!