Can someone give me an example of a group which has exactly $2$ proper, non-trivial subgroups?  I appreciate that there is no context with this question but there's no really much else I can say.
Suppose $G$ is a group and has exactly two nontrivial proper subgroups. Prove that $G$ is cyclic and $|G|=pq$ where p,q are distinct primes or $G$ is cyclic and $|G|=p^3$ where $p$ is a prime. Usually my tactic to show a group is cyclic is find an elements such that its order and order of the group are the same. But here I cannot do so because I have no informatio regarding order of elements. So I stuck. Can anyone help me?
On the  it is mentioned that it is not a Cayley graph.    How it this proved? Honestly I don't even know how to start this. The only criteria I can think of is that all vertices must have the same degree. Also the degree being odd should imply that one generator of the group has order 2. But then how do I proceed?  Edit: As already mentioned in the comments, the link did not answer my question. When I parent an object to follow a path and animate it, I only get a linear mode animation and changing that in Grapth Editor to bezier doesn't work! How to do that? How do I get the deformed coordinate of a vertex with Python? How might someone find the deformed coordinate via Python or otherwise when using a subdivision modifier with the 'show on cage' option?  For example, a subdivided cube with cage enabled and a vertex selected shows the location of the vertex at 1,1,1 but when manually placing the cursor near on the surface it is closer to .5,.5,.5  I know the vertex location needs to be at its non-deformed location for subdivision to even work but would like to get more accurate point locations at the surface without having to apply to mesh. Was Philip K. Dick able to watch a complete version of Blade Runner before his death or just unedited material?  The Blade Runner release date according to  and IMDb was 25 June, 1982. Philip K. Dick died a few months before, on March 2, 1982. Scorched3d worked then stopped. Unistalled and reinstalled did not help. Running Ubuntu 16.04.04LTS. I think it was after installing new release.  I think the problem is the Ubuntu 16.04.4LTS. The newer version has no Scorched3d in the Ubuntu Software Center. I have 3 systems. After updating to new version. Scorched3D will not install and work after updating.  ron@RonsComputer:~$ sudo objdump -p $(type -p scorched3d) | grep NEEDED  NEEDED libwx_gtk2u_adv-3.0.so.0  NEEDED libwx_gtk2u_core-3.0.so.0 NEEDED libwx_baseu-3.0.so.0 NEEDED libfreetype.so.6 NEEDED libz.so.1 NEEDED libSDL-1.2.so.0 NEEDED libSDL_net-1.2.so.0 NEEDED libexpat.so.1  NEEDED libstdc++.so.6 NEEDED libm.so.6 NEEDED libgcc_s.so.1 NEEDED libpthread.so.0 NEEDED libc.so.6   ron@ron-desktop ~ $ objdump -p $(type -p scorched3d) | grep NEEDED | awk '{print $2}' | xargs -n 1 dpkg -S  libwxgtk3.0-0v5:amd64: /usr/lib/x86_64-linux-gnu/libwx_gtk2u_adv-3.0.so.0.2.0 libwxgtk3.0-0v5:amd64: /usr/lib/x86_64-linux-gnu/libwx_gtk2u_adv-3.0.so.0 libwxgtk3.0-0v5:amd64: /usr/lib/x86_64-linux-gnu/libwx_gtk2u_core-3.0.so.0.2.0 libwxgtk3.0-0v5:amd64: /usr/lib/x86_64-linux-gnu/libwx_gtk2u_core-3.0.so.0 libwxbase3.0-0v5:amd64: /usr/lib/x86_64-linux-gnu/libwx_baseu-3.0.so.0.2.0 libwxbase3.0-0v5:amd64: /usr/lib/x86_64-linux-gnu/libwx_baseu-3.0.so.0 libfreetype6:amd64: /usr/lib/x86_64-linux-gnu/libfreetype.so.6.12.1 libfreetype6:i386: /usr/lib/i386-linux-gnu/libfreetype.so.6 libfreetype6:amd64: /usr/lib/x86_64-linux-gnu/libfreetype.so.6 libfreetype6:i386: /usr/lib/i386-linux-gnu/libfreetype.so.6.12.1 zlib1g:i386: /lib/i386-linux-gnu/libz.so.1.2.8 zlib1g:amd64: /lib/x86_64-linux-gnu/libz.so.1 zlib1g:i386: /lib/i386-linux-gnu/libz.so.1 zlib1g:amd64: /lib/x86_64-linux-gnu/libz.so.1.2.8 libsdl1.2debian:amd64: /usr/lib/x86_64-linux-gnu/libSDL-1.2.so.0.11.4 libsdl1.2debian:i386: /usr/lib/i386-linux-gnu/libSDL-1.2.so.0 libsdl1.2debian:i386: /usr/lib/i386-linux-gnu/libSDL-1.2.so.0.11.4 libsdl1.2debian:amd64: /usr/lib/x86_64-linux-gnu/libSDL-1.2.so.0 libsdl-net1.2:amd64: /usr/lib/x86_64-linux-gnu/libSDL_net-1.2.so.0 libsdl-net1.2:i386: /usr/lib/i386-linux-gnu/libSDL_net-1.2.so.0 libsdl-net1.2:amd64: /usr/lib/x86_64-linux-gnu/libSDL_net-1.2.so.0.8.0 libsdl-net1.2:i386: /usr/lib/i386-linux-gnu/libSDL_net-1.2.so.0.8.0 libexpat1:i386: /lib/i386-linux-gnu/libexpat.so.1.6.0 libexpat1:amd64: /lib/x86_64-linux-gnu/libexpat.so.1 libexpat1:amd64: /lib/x86_64-linux-gnu/libexpat.so.1.6.0 libexpat1:i386: /lib/i386-linux-gnu/libexpat.so.1 libstdc++6:amd64: /usr/share/gdb/auto-load/usr/lib/x86_64-linux-gnu/libstdc++.so.6.0.21-gdb.py libstdc++6:i386: /usr/lib/i386-linux-gnu/libstdc++.so.6 libstdc++6:amd64: /usr/lib/x86_64-linux-gnu/libstdc++.so.6 libstdc++6:amd64: /usr/lib/x86_64-linux-gnu/libstdc++.so.6.0.21 libstdc++6:i386: /usr/lib/i386-linux-gnu/libstdc++.so.6.0.21 libstdc++6:i386: /usr/share/gdb/auto-load/usr/lib/i386-linux-gnu/libstdc++.so.6.0.21-gdb.py libc6:amd64: /lib/x86_64-linux-gnu/libm.so.6 libc6:i386: /lib/i386-linux-gnu/libm.so.6 libgcc1:amd64: /lib/x86_64-linux-gnu/libgcc_s.so.1 libgcc1:i386: /lib/i386-linux-gnu/libgcc_s.so.1 libc6:i386: /lib/i386-linux-gnu/libpthread.so.0 libc6:amd64: /lib/x86_64-linux-gnu/libpthread.so.0 libc6:i386: /lib/i386-linux-gnu/libc.so.6 libc6:amd64: /lib/x86_64-linux-gnu/libc.so.6 ron@ron-desktop ~ $ In my script, I have for loop over many cube objects (~1000) and the treatment is very slow. Looking more in details, I notice that in the same amount of loops:   if I use python operation or simple blender operation like  obj = bpy.data.objects[obj_name]   or   obj.select = True   it takes less than 0.08s (for all 1000 objects) but as soon as I start using blender operators like:  bpy.ops.object.select_pattern() # or bpy.ops.object.duplicate() # or bpy.ops.object.location_clear() # or bpy.ops.object.transform_apply() # etc.   then, the performance drops down deeply with more than 6s for the same amount of objects.   And, a last information, if I reduce the amount of objects from 1000 to 50, the same set of operations with bpy.ops is 0.03s - so extrapolating, it would be 0.6s for the 1000 objects and not 6s. It is as is with 1000 objects, we loose a factor 10 in speed in comparison than with 50 objects.  I tried reducing the complexity of my mesh changing the cubes in planes but it had no effect at whole on performance.  Is there something particular to know to improve these performance or a way to use the bpy.ops methods with better performances? Obviously, I am missing something important probably. I've seen a contraction of two words.  I can't see why it wouldn't've been possible to have been contracted twice.  Is it possible and how should it be punctuated?  Update:  Ok, to sum up the answers so far   This appears in spoken British and American English It is from one of the lower  Even if spoken this way sometimes, it isn't really written as a double contraction, except as written speech in fiction. And from my own googling in , it appears most written forms are old British words, often nautical like fo'c'sle. Is there a reason to use multiple question marks instead of an asterisk in filename expansion? If I have a number of directories, named, for example 10001 through 10025 is there any reason to use ls 1*/foo vs. ls 100??/foo?  I have a lot more than 25 of them, so I mostly curious if there's any differences in speed.  I know the difference in use between the two, that the asterisk will match longer file names, like 10001.backup. But let's say I don't have any files that don't follow my conventions. Is there any behind-the-scenes differences? Is it pythonic for a function to return multiple values? In python, you can have a function return multiple values.  Here's a contrived example:  def divide(x, y):     quotient = x/y     remainder = x % y     return quotient, remainder    (q, r) = divide(22, 7)   This seems very useful, but it looks like it can also be abused ("Well..function X already computes what we need as an intermediate value.  Let's have X return that value also").  When should you draw the line and define a different method? In Windows, you can run android application using BlueStack.   I was wondering, is there any way these apps can be run on Ubuntu 12.04? Clean install of Windows 10 OEM: license key issues? Proof of Dobinski's formula for Bell numbers How to evaluate potential advisers on grounds other than their research/publications? While accepting an offer to grad school, one is basically entering into a lasting relationship with one's adviser - most likely, someone whom the applicant has never met before, and the only exposure has been through the potential adviser's website/publications. It is in the interest of both parties to ensure (to the greatest possible extent) that there are no personal/professional traits of either that hamper the formation of a pleasant working relationship - no-one would want to go through the ordeal of having to change advisers midway!  While the faculty has a chance to have a good look at the applicant's profile as well as his motivations (through his grades and SOP), the applicant doesn't have a similar opportunity. So, I'm interested to know what parameters can be used to gauge a potential fit. I've thought of the following:   Past students:  Did anyone ever drop out/change advisers midway, and if so, for what reasons? These would be a bit hard to find though, as I don't expect the faculty concerned would list them on their website. It would be great if anyone could let me know how to find out the list of incoming students to a department for any year. Publication rate, taking into account the venues where they were accepted. Time taken to graduate - though I accept this is more dependent on the student, a median figure should be telling ... What they did post Ph.D. - did anyone get tenure if they went into academia, or is almost everyone unable to break out of being a post-doc?  Tenure status: I'm a bit unsure about this, so wanted the community's opinions about it. Just so that I'm clear, I'm only trying to calibrate the applicant's expectations about the working style of his potential adviser - and hence need to know to what extent are the following "typical" assumptions valid.  Tenured professor  A full professor is more likely to get grant funding, hence less time spent on TAship - but could also mean less time/effort spent on interactions with students (either being busy with other projects/talks, or due to more commitments to family at that age).  Tenure-track faculty (Assistant profs)  More likely to be young and energetic, and could translate to more time spent on one-to-one discussions with grad students - but funding may prove to be an issue, and may have to be on TA for a longer period.   What other factors would be relevant in this matter, and to what extent am I correct/incorrect in either the factors considered, or for undertaking this exercise at all? Is there a slowest rate of divergence of a series? $$f(n)=\sum_{i=1}^n\frac{1}{i}$$ diverges slower than $$g(n)=\sum_{i=1}^n\frac{1}{\sqrt{i}}$$ , by which I mean $\lim_{n\rightarrow \infty}(g(n)-f(n))=\infty$. Similarly, $\ln(n)$ diverges as fast as $f(n)$, as $\lim_{n \rightarrow \infty}(f(n)-\ln(n))=\gamma$, so they 'diverge at the same speed'.   I think there are an infinite number of 'speeds of divergence' (for example, $\sum_{i=1}^n\frac{1}{i^k}$ diverge at different rates for different $k&lt;1$). However, is there a slowest speed of divergence?  That is, does there exist a divergent series, $s(n)$, such that for any other divergent series $S(n)$, the limit $\lim_{n \rightarrow \infty}(S(n)-s(n))=\infty$ or $=k$? If so, are there an infinite number of these slowest series? Is adjoint of singular matrix singular? What would be its rank? Introduction to Statistical Learning defines the F-statistic as follows: $$\frac{(TSS - RSS) / p}{RSS / (n - p - 1)}$$ I am trying to interpret this formula intuitively - the numerator looks like the $ESS$ per regressor, and the denominator looks like the $RSS$ per observation. This does not seem like an apples to apples comparison; can anyone explain why it makes sense?  They also say that the expectation of the denominator is equal to the variance of the irreducible error if the linear model assumptions hold (I get this, as the denominator is really the Residual Standard Error, which is an unbiased estimator). They also say the numerator is equal to the variance of the irreducible error if the null hypothesis is true. Therefore the F-statistic will be close to 1 if the null hypothesis is true.  But if you let p = 1, that is, apply the F-statistic to single linear regression, it becomes:  $$\frac{TSS - RSS}{RSS / (n-2)}$$  According to the book, if the regressor has no explanatory power, the F-statistic should be close to 1. But if you imagine a data set where the coefficient on X is 0 (i.e. no explanatory power), $TSS$ will be equal to $RSS$, so the numerator and hence the F-statistic should be 0, not 1 as they claim. What is going on?  Furthermore, if you accept that the F-statistic is 1, as they claim, then $(TSS - RSS) = RSS / (n-2)$, which means $ESS = RSS / (n-2)$. If you think of the F-statistics as comparing explained vs. unexplained variation, this does not seem like a fair comparison since this decomposition makes it the ratio of TOTAL explained variation summed across ALL observations vs. the unexplained variation PER observation. Again, what am I missing?  I am just trying to make sense of it in a layman way, apologies if I am missing something obvious. Is it a problem if a UK visa was issued but not used? Last year, my wife and I were issused 6-month visieor visas for the UK. She did not travel with me and, therefore, didn't use her visa. I am currently applying for a visitor visa for my daughter and myself.  Will the fact that my didn't use her visa have any negative affect on our new application? Get latest Flash player on Ubuntu I know, it's been asked before but I couldn't really get a satisfying answer for some details/backgrounds and I guess it's an important question for many.    Some application seem only to be running with Adobe Flash 15 (or at least I know it does, because I have that version on my Windows Partition).  The official Adobe website says:     NOTE: Adobe Flash Player 11.2 will be the last version to target Linux as a supported platform. Adobe will continue to provide security backports to Flash Player 11.2 for Linux.   Some search on the web like "Ubuntu Adobe Flash 15" or similar does not return any good websites.  I found something that says   (using a "pepper-based version"), and  .   Is it impossible to use this for Firefox too? Would it be a privacy risk?  Are there no alternative projects (I know it's closed source but there are so many so very bright people out there using something similar to wine but just for the plugin....)?  How about the Mac-Version? Shouldn't someone be able to port that one to Linux? Lots of ram. How to use it? My PC has 8 Gb of ram. Is there any way to make ubuntu use most of it? I mean rarely drop caches and keep once opened programms in ram longer, preload apps on boot, etc. How to check if a row exists in MySQL? (i.e. check if an email exists in MySQL)